paternity (fathership) test

Mama Allpa aims for realism. Hence the fathership can only be determined when

•  the potential father is present during the test
  OR

• the potential father has set his male Mama Allpa HUD to "public father". In this case he does not even need to be online. Enabling and disabling this feature can be done by the male at any time, regardless of the females he was intimate with

Also you have to be in a confirmed pregnancy, in a human setting this is past day 24. Trying to run paternity tests or pregnancy tests before that will produce no results.
To run a paternity test you can either use the free test tool at the mainstore, use the physician bag or consult a Mama Allpa Physician. 

To use the free test tool or to consult a MA Physician, click in your HUD "Help" and "Doctor Appointment": you will get a teleport offered to the contact panels for our staff. the test tool is right beside these contact panels - see the picture below for how the panel looks like

What if the paternity test says that the mother is also the father?

this occurs when you have set yourself manually to pregnant, ignoring the warnings that the HUD gave you while doing so. If you want to have a self-set pregnancy, no other person can be the father.