Wanted interactions: ff6, 8, 9, Fallout, TWD, TLOU, historical/modern fandoms that I know & Doctor Who (have their full AU verses written), and has adaptations for One Piece LA and manga to the end of Whole Cake, Dragon Age, LoTR, Grishaverse, Squid Game, fantasy fandoms, alien-friendly fandoms. 

Open to ship with: in canon Locke, Edgar, maybe Setzer, and chemistry-based elsewhere. She's definitely demiromantic and demisexual with a lot of confusion about how love works. More oriented towards men but can fall for women too.

Terra's whole thing in her own canon universe is that she's Special. She's a weapon of mass destruction, she's not entirely human but the more she chooses that side and the happier and stronger she becomes, not to mention more in control of what she does. That's her thing.

So this backstory starts after the gross guy from West-tek suggests 'what if we experiment on illegal immigrants in my Vault'. She can fit into this universe as a Chinese child who was literally kidnapped to be in Vault 4, born PRE-war, and was experimented on for years, raised as a slave who would just let them do what they wanted, and she was given extra organs and parts, had an arm taken from a deathclaw and made to look human, to become a weapon herself.

From age 8 to 18 they built the body, and she was also taught enough a functional weapon when needed (which includes speaking/reading English). She wasn't entirely isolated for the same reason, but mostly what keeps her sane later on is that she doesn't remember most of it.
And then they made a mistake and put her in cryo. Kefka, the lead doctor, puts himself in cryo too so he can keep working on his Esper project. 

The mistake in question, the ONE special thing she can have to replicate her canon, the one "super power" that would make her different from everybody else and that had Vault 4 scramble to put her in a cryo machine, would be radiation. Having the ability to shoot radiation at people/become as radioactive as a bomb, to the 'melting body' level, which can happen against her will when she truly feels hatred/rage against a person or not against her will if she's protecting someone else. She's not in control of it because she doesn't want to be, but she could have been a human nuclear reaction (except she'll never be because if her heart is not in it, it doesn't work, pesky side effect of human experimentation not going as the doctors wished).

Around 200 years later she's awakened by Kefka, and brought to the Enclave, which from my understanding is where they do experiment that include behavioral control, and she stays there, from age 18 to 24, trained to be a mindless assassin. The necessary interactions with humans and lessons on how the world works, though, start making her want to escape. To have more than that. To be alive and free. She was never taught how to summon her abilities because she only has to use them when controlled.

Until they push her too hard and she literally melts a bunch of scientists and runs.
Radiation obviously doesn't affect her, she has random skills due to the body parts she was given that at the beginning she doesn't know how to use, including the fact that she still has the deathclaw arm (normally it's stronger than the other but she doesn't know how to make it deathclaw-strong, but this one is something she may be able to summon eventually) and that sometimes she can see in the dark. Usually that means she's nearly useless in a fight until the arm or the radiations kick in. 

There is a giant bounty on her, and she only remembers her name and some of her time at the Enclave and Vault, but after a while she also starts remembering more, even life before war, which is very confusing when looking at the Wasteland, and now is trying to figure out what she is, who she is.

But here's the kicker: people involved in the Esper Project (as in Terra having been given the radiation ability and several more that could make her a one woman army), have a song that can re-activate her, and she'll be back to brainless slave while it's playing/being sung. She can be awoken when it stops playing or, later on, by trying to reach her human side if there is a bond. Her Esper moment lowers her ability to feel pain and gives her full control of her 'custom abilities', however she only uses as much as needed to complete the mission. The song could be Elvis Presley's Jailhouse Rock as a reference to the fact that Fallout couldn't afford those songs and we don't normally hear Elvis on the radio.

She doesn't want to hurt anyone or fight, but will take upon herself to defeat the ones involved in the Esper Project and/or whoever the enemy is once she bonds with a person or a team, following her canon path of 'starts as the main hero who actually doesn't want to do anything and ends as someone who finally understands love and that makes her finish a war'. 

Adores animals, would have a pet molerat eventually (to replicate her canon dynamic with moogles), likes sugar, unlike radiation alcohol does affect her and she doesn't like it, likes the rain, the beach (some of her last good memories were there, though obviously now it's not the same), 

Note that in canon her happy ending is becoming the Mother in a village of children left orphans by the end of the world, and that teaches her what love and humanity is. Love is what saves her (also maybe adopting an entire vault of kids)

When it comes to the real world, since there is no magic and no way to turn a human being into a weapon of mass destruction, the only thing that can make her so "special" and still b a weapon of sort is being a genius, and able to create bioweapons/replicate any code she sees. And she can be famous over what I'm about to describe, for Dramatic Purposes.

She's kidnapped as a child due to showing signs of being that gifted, and her father is still part of an extremely important family with many enemies like in canon, which is also why Kefka (the Bad Guy) is able to keep tabs on them and take the kid to experiment on her, try to enhance her brain, make her do as he pleases and eventually torturing her as a punishment too, on top of doing it to figure out how to enhance her body and mind.
Mostly she dissociates and loses memories, which is what allows her to not fall apart entirely, and she's taught the least necessary to make her eventually function as a weapon, as well as what they need her to know to help in her biochemistry projects. That means obviously severe lacking of knowledge of how people/relationships/emotions work, outside of a few books she's read, and of connections, yet her personality is what you read above.

They also start training her as an assassin of sorts in the sense that she needs to be able to fight her way in and out of places for their missions, but she only responds when she's in a 'trance' that is really a defense mechanism against what they are doing, she wouldn't be able to fight unless her bosy/muscle memory kicked in while her brain, for a lack of better words, checks out.

She's 24 when she snaps, and in one moment she causes the releasing of gas that kills dozens of people in that facility and runs. Depending on what we need in our universe, she's left that world behind except for Kefka who wants her back (but he can be killed if we want to focus on nice things), and some of the surviving members of the project are trying to capture her again, so she's on the run and or being rescued when she gets to your muse.
Her hair is still blonde, btw, due to chemical reactions in her body caused by experimentation.
Trauma, brainwashing, and hitting her head at some point when running away make sure that she only remembers her name initially, and having flashes of memories + hearing what has been said about her, which brings us back to her not wanting to fight but also changing the more she can remember, but depending on what universe we write in she can be past memory loss, or past most of it.

In Bridgerton: after soldiers take care of Kefka, they bring Terra to the queen, who takes pity on her (she can see the signs of torture, and they are uncomfortably similar to what she saw on George's body after saving him from his doctor) and has her temporarily under either Lady Danbury or Lady Bridgerton's care so that she can learn how to be a person again. 

In Turn WS: obviously she can just be rescued by the army of your muse. 

In Chuck: she's found by the team and given her incredible knowledge of Kefka's criminal organization she has to stay and help, because there is no data in the Intersect and they are a problem.

Firefly: obviously she was kept in the same facility as River, but longer because of Kefka's fixation on her. 

Any cop show or Leverage or Lost: nothing needed to change. 

The only difference from the main backstory would be that she's not an esper but instead was born from two people who ate the Devil's Fruit, to give her that 'she's super special' trait she has in her own canon without stealing a protagonist role.

For this reason her body is more 'adaptable' to the fruits' powers, and Kefka stole her as a child and started experimenting on her with very advanced techniques, to try to give her copies of certain abilities, which are therefore man-made and not subject to devil fruit's limitations but also not as powerful; the same way we have seen Germa 66 and Ceasar transform children into something more.
Her body is sort of a 'build your own doll' object to him, but he cares about "the aesthetic" and tried to create limbs that look like hers, so what's visible is that she has scars everywhere as if her body has been stitched together.
This means she gets random powers at random times (due to One Piece's Science): the most commonly used are fire (not as strong as the one Ace/Sabo have, it's more about dropping a fireball on people) and producing wind/flying when she does, to homage her own canon, but she can't fully control them. She can of course skip so super strength like the Vinsmokes (again, out of her control), and occasionally use other elements.
She's technically extremely dangerous, wanted by the marine and by villains who intend to use her, and extremely not here to fight. She hates it.

Kefka mind-controlled her for years, forcing her to mass-murder people for him until she accidentally broke the slave-crown he used to enslave her, and her first instinct was to run and hide, though due to her explosion of emotions she left a giant trail of bodies behind. She does partially remember being experimented on and being trained to be an assassin, and is terrified to go back, as well as extremely confused about how the world works. 

She's sweet, friendly, terrified, trying to find out who she is and what she wants, running from Kefka and his people, and generally trying to understand the rules of society, so she's very open to be 'changed' by your muse (she is the type to say 'you are being comforted' when patting someone's arm because she's seen that gesture done before and is trying to copy people and manifest her intentions with words).

To respect her canon story in which she's THE Special One, while still letting Ellie be the PROTAGONIST of TLOU and/or leaving the world without a cure like in TWD, Terra is partially "immune" (but not really); her immunity is different from Ellie's, as is her fate, so I'm going to try to translate her canon story into tlou-appropriate. A very similar type of immunity has been written for my @justaprankhan too because I wanted to explore it on someone with the opposite personality, and we can assume they could exist in the same universe: 

To anyone who hates the idea of another immune person (valid) I offer the option of Terra being an Infected person who can infect others with her blood but has retained her mind, and the various experiments have been done not only to study her but to remove the cordyceps parts that were growing in her body/fix parts that were starting to (very slowly) rot. I may ask you which option you prefer if we plot, but if I don't, for any reason, you can straight up tell me!

Her immunity consists of her immune system being able to fight the infection the same way we can get the flu every year, get sick and then it's gone: due to a special mutation of her DNA her body lets her heal within a day, and it cannot be replicated/used to make a cure because her DNA mutation is required for it to work. She's also contagious while feverish, and her body gives off a scent that other Infected recognize as 'one of their own' so they won't try to bite her (but fight back if she attacks first).
This was noticed immediately upon birth, after she was taken from her infected mother, who was wandering around the room looking for humans to bite while baby Terra cried on the floor, healthy-looking, and so the child was put under watch by what was left of the government. 

A scientist named Kefka takes full control of Terra and starts experimenting on her. His taskforce is not above vivisection; she grows up in a lab, she's given some human interaction because they need her to function so that she can not only answer their questions but, eventually, be trained to become one of their weapons, since she can be sent through hordes of Infected easily, and for that she needs to be able to interact with them, too bad that she's the least bloodthirsty person they could've found. 

One of her arms is cut off for studying after being infected, replaced by a bionic one. One of her eyes is taken out too after subjected to infection, and replaced as well. This is alternated with classes to learn a bit about how the world works or being put in comas as needed.
By the time she's 18, it's clear that her immunity cannot be replicated and cannot lead to a cure. If she were to be temporarily infected with a bite she could infect people (until her body heals).

She's supposed to become one of their Operatives until the day she snaps. She goes to one of the 'Danger Rooms' where she gets trained to sustain the effects of being temporarily infected, collects spores/blood (depending on the fandom), and runs. On her way out, she simply throws the spores/blood at people like confetti.
She regrets it, never wanted to hurt anyone, and Kefka isn't even there to pay for what he's done, but she's finally out. No idea of how to be around people, learned most of what she knows from books, terrified, partially expecting more torture, but out. 

in tlou: Any character could find her while she's on the run (this to also include people like Tess and others who are not there in canon later, and ocs), but to justify why other canon ones may have interactions with her, we could say that she did end up in Abby's father's hands before Ellie, one of the immune people mentioned in the medical notes, but given her 'report' and physical proof of what was done to her, plus his studies, it was almost obvious that she can't produce a cure. Plus, the potential Cure in form of Ellie was coming over soon, so she was put aside for further investigation and managed to escape again when Joel started killing everyone at the hospital.
So now she wants to find this Joel because she's seen what he's done to get the next immune girl out and therefore he seems the safest person to be close to, OR if you are writing Abby's group, Abby would know who she is and that she's 'useless' but also so lost. Kefka is obsessed with her, she's his jewel, and wants her back.

in twd: she's free to meet anyone at any point!

Terra, daughter of Ordinarium's Master (but she can be the daughter of your Master too if you want, parallel universes exist and it doesn't change his storyline besides 'he had a baby and was told she died with her mother'), was taken as a baby from her mother, who was murdered in the process, by Rassilon as his personal vendetta against the Master over being attacked and forced to regenerate by him (after the Tenth Doctor ended their plans and sent them back to Gallifrey). The Master was told Terra had been killed, meanwhile she was taken by the scientist Kefka, who began experimenting on her and became obsessed by her and the idea of making her into the most powerful weapon of mass destruction.
His studies were meant to test the regeneration boundaries and powers of the first generation of Gallifreyans who were born with that energy, and being the daughter of the Master, who was one of the first ones Tecteun had 'gifted' with the ability to regenerate, she was perfect for it; she died and came back countless times, she was experimented on, enslaved with a crown that controlled her thoughts, even taught how to be an assassin (it didn't stick); in a way being left almost mindless was what gave her the chance to mentally survive the torture. The 'super special power' she gets, to give a homage to her canon counterpart, is that she can *use* her regeneration energy to blast and burn/melt everything around her whenever she wants, but she'd rather get more tortured than do it.

One day the slave crowns breaks by accident, and in a moment of despair, of wanting to hurt the people around her and escape, she lets out the biggest explosions yet, which tears down half of the building and kills nearly everyone. Kefka survives, she runs through the burned bodies and finds herself in New New (etc...) New York, on New New (etc...) Earth. 

There she can be rescued by anyone if your muse is a space-traveler, or, if you want to interact with her on Earth/past etc, she has been already rescued by my Jenny (the Doctor's daughter) and left under Unit's care. Except for the verse where her dad finds her first and takes her with him.
Other Masters are welcomed to interact (in a non-murderous capacity possibly?), it could be a parallel universe Master or regenerations and so on.

Terra, like I said in her personality's paragraph, will *not* be up for murder at all, except when truly forced or defending others, and initially is more used to being considered a slave, an object, or a monster, that she'll kept expecting the same treatment and looking around for guidance. Eventually, once she learns her own personality and worth, she'll become more independent and finally evolve into her Main Character persona, who will fight to protect others. She's also a sweetheart with very little understanding of how society and relationships work, since she never had them before, and while her brain works just fine, she will come off as weird/awkward at times or be the person who says whatever she's learned to be 'supposed to be comforting' without knowing what it means.

Created in collaboration with @retrograderesemblance.

I didn't want Terra to be a Sun Summoner since that's Alina's thing, nor anything else that is meant to be other characters' unique trait, so I came up with a slightly different "special" thing for her: she was the daughter of a Sun Summoner, who existed before the Darkling's era, and of a Grisha who had enhanced her powers with amplifiers.
She was frozen in time (and literally frozen) by long lost magic as a baby, and freed by a king who gave her to Kefka, to be experimented on soon after it became obvious that Terra has the ability to manipulate multiple elements (which is also literally what she can do in her canon). That's her unique thing, she can manipulate air, dirt, fire (her special), water, blood, and so on.
For that reason she was considered more of a monster than a Grisha, one of legends but one without rights none the less, and Kefka used the slave crown to control her and move war in this verse too (the slave crown can easily be an amplifier that bound her to him).
But once they reached the fold her blood resonated with that kind of magic, and allowed her to go free from the crown and from Kefka. She doesn't know who she is besides her name, she remembers the experiments and torture soon, but your muse can find out when interacting with her and tell her (and I'm assuming that Aleksander and family know about the story even if they couldn't find her in their time because she was transported far away and it was no priority of theirs).

Her loyalties will lay with who is nice to her and convincing, but obviously she sides with Grishas being treated better than they are, given that she can see herself in them.  

she was kidnapped as a baby by some crazy guy (Kefka), part of an organization who already had a war going with her parents; he trained her to be a monster/killer and completely failed to make her want to kill people, physically tortured & emotionally abused her to make her his 'perfect weapon', and then she ran off after killing a bunch of his people, traveled low-cost or stole to get away, ended up homeless in south korea, tried Ddakji and joined the game to get money but also she has no clue of what's going on or how to be a person yet, and this is the absolutely worst possible way to find out. So that's fun.
She votes out, but also when push comes to shove she absolutely murders people in mingle even if she hates it because it's either them or her allies. Mostly season 2-3 based because I think that's where it's more interesting since she can display her murder-skills there, even if she hates killing (but she will kill to protect others, it's what she's 'built' for and she'll use it).
number 010.

Looks-wise: I wanna say she dyed her hair black to be less recognizable but she's so cute blonde? 

She could easily be in Dragon Age as a part spirit/demon (since they are technically the same) which justifies why she's so 'special' and is Kefka's mindless slave until freed. So her general backstory can be adapted to Thedas, with a mage (Kefka) using her as his weapon of mass destruction and who is also drawing from her powers to give magic to his followers.
It would follow her canon backstory, but leaving it open ended because there is no world destruction by the villain and no reason for her to lose her magic/spirit side.

She'd still lose her slave-crown and be found by your muse or people close to your muse, and could be an important part of whatever battle they are fighting, if it wasn't for the fact that initially she doesn't want to be part of any war, she wants to learn who she is, what she wants, and not kill people. But the mage is sending people after her because she's too precious, so not fighting may not be an option.

She could easily be half demon, which justifies why she's so 'special' and is Kefka's mindless slave until freed. So her general backstory can be adapted to this world, keeping in mind that I only reached the beginning of act 3 and then my laptop died, with a mage (Kefka) using her as his weapon of mass destruction and who is also drawing from her powers to give magic to his followers.
It would follow her canon backstory, but leaving it open ended because there is no world destruction by the villain that I know of and no reason for her to lose her magic.

She loses her slave crown on the Nautilus when given the tadpole, and can be found wandering near the site of the crash, completely lost and terrified, ready to buy whatever the other person says and in need of all sorts of guidance; she doesn't want to fight, doesn't know what she wants except not to be hurt anymore, getting memories of her torture/experiments as she goes. That means she stays mostly at camp, seemingly helpless, until someone she cares for is threatened or someone is about to take her back to Kefka, and that's when her power of absolute destruction is revealed. She doesn't want it, though, and she'll need to first understand what it's like to bond with people and caring before choosing to truly get into the fight and dirt her hands. 

Her story can remain exactly the same to allow more interactions, with her lands being in another continent surrounded by water, which also allows for Kefka to break it into pieces here too. Regardless, your muse will be the one around her while she learns how to live and who she is.

Depending on your fandom, she will still be the daughter of a magical creature and a human, and the magical creature must be a rare/ancient one to explain her 'excess' of power and changing form. 

She could be half alien in marvel and dc, nearly same story, with Kefka, a bad guy from Hydra (Marvel) or Cadmus (DC), having taken control of her. Everything else stays the same: slavery, freedom, lack of memories, learning how to live. 

She could adapt to most modern verses that allow magic too the same way, still with the formula of: Kefka enslaves her, and her father is part of an ancient and extremely powerful race, or if we want to stretch it and there is no magic, she could be mind-controlled with some device that is verse-dependent and used as the perfect killer.

Since in her original backstory she's meant to be 'extra' special by having innate magic in a world that is nearly magic-less, and extremely powerful at that, instead of making her your "more common" noble half-elf, I think the closest thing to creatures like espers would be an ancient race of dragons, now gone, that can occasionally change into human/elf form. Which would make her father Maduin a dragon, and maybe her mother Madeline an elf.
They are able to have Terra right before an evil wizard catches them unprepared, and we can still call him Kefka. He's an outsider with great power, and even more so when she takes Terra under his control.
She's free by the closeness to another dragon who doesn't attack but leaves, and it awakens her ability to turn into a creature similar to it. 

The rest of the story can follow "canon", with your muse being the one around Terra as she tries to learn her place in the world after she falls into their lives by accident, possibly escaping Kefka's orcs. 

I'M WILLING to change details to make her fit better into your muse's headcanons/world given that her parentage may not fit.