All of the relationships in this section are purely speculation. They are based on a few census records, which is the extent of the known data on this family group. I would eagerly accept supplements or corrections to these theories based on more substantive data such as Bible records, wills, anything!
As best we can determine, Joseph and Nancy had at least two sons: Josiah and Jesse. They may also have had two other sons: Arthur and John. In a somewhat significant departure from the usual Kerley naming practices of that era, Joseph and Nancy seemed to enjoy naming their offspring names that began with the letter "J" (as seen below). And, those kids continued their parents' tradition - there are a lot of Kerleys whose first names begin with the letter J in this family. This family was the last one to leave the original Kerley settlement in South Carolina. And, unlike the other original Kerley settlers, they moved primarily to the South (Alabama, Mississippi and Texas).
Josiah3 (Joseph2,William1). Josiah Kerley was born about 1760 in South Carolina. He appears for the first time in the 1800 census for the Sumter District of Clarendon County, SC., not too far from the listings for his father (Joseph) and his brother (Jesse). Although Josiah is listed as living alone and being between 16 and 26 years old, I am pretty sure that this entry is incorrect. The 1830 census for Monroe County, Alabama shows Josiah as being between 60 and 70, and the 1840 census for that same county shows Josiah as being between 80 and 90. These latter two records place Josiah's birth date as sometime around 1760. So, I suspect that the census taker for this this 1800 census entry probably checked off the wrong column. Josiah moved to Monroe County, Alabama around 1817 and raised his family there. After this move, the family adopted the Kearley spelling. All of Josiah's children (as evidenced by their gravestones) used this spelling.
Jesse3 (Joseph2,William1). Jesse was born about 1769 in South Carolina. He appears for the first time in the 1800 census for the Sumter District of Clarendon County, SC, not too far from the listing for his father (Joseph) and his brother (Josiah). (His entry is immediately after Joseph's and just a few entries from Josiah's). At that point in time, Jesse had one son under 10 (name unknown) and two daughters (both under age 10 and both names unknown). Jesse and his wife are both listed as being between 26 and 45. So, it looks like they got married around 1790 and had 3 kids during the 1790's. Jesse would have thus been around 25 when he married and started having a family in the early 1790's.
The weakness in this theory, however, is that Josiah and Jesse were old enough to be listed in the 1790 census, but they do not appear there or appear to be living in Joseph's household. I am not sure where they were in 1790. Were they out exploring? Were they simply missed by the census-taker? Were they living as farm-hands with a neighbor? We will probably never know.
Arthur3 (Joseph2,William1). Arthur is one of the more well-documented Kerleys. His death is recorded in the federal census mortality schedule for Lauderdale county, Mississippi in 1850. That record confirms that Arthur was born in South Carolina in 1785. At that point (1785) most of the members of the second generation of Kerleys had moved out of South Carolina, and as far as we are aware, the only remaining member of that original group of settlers who still lived in South Carolina was Joseph. Far that reason, I believe that Arthur was the son of Joseph.
Arthur apparently stayed in the Camden SC area for the first 40 years or so of his life. Local records there confirm his presence there until the late 1820's. There are records indicating that he served (with his brother, John) in the War of 1812. See War of 1812 page Other records confirm that he (along with a person named Daniel Kearly) bought a slave in 1819. He shows up in the 1820 census (as Arthur Carely) in Sumter County, South Carolina (1 male 26-45, 1 male under 10, one female 45 and up and one female between 10 and 16). In 1823 he bought 305 acres of land in Sumter Co., SC. (That raises the question of where Arthur was living before that. Was he still on the old Kerley family farm there in Sumter Co.?)
He also went in on some type of partnership and he and two guys named Cantey bought 85 acres in nearby Clarendon County, SC, the next year in 1824. Local records mention that his children (Caroline Mary, John Jackson, Elizabeth Theresa and Joseph Washington) were given a slave in 1824. Arthur also witnessed a neighbor's will in 1828. Based on the ages of his children it looks like Arthur got married about 1815. He married a woman named Sarah Barrett. (There are several Barretts listed on the same page as Arthur in the 1820 census.)
Sometime in late 1829 or early 1830 Arthur decided to abandon the Kerley settlement in the greater Rimini area. He thus became one of the very last (if not, in fact, the very last) Kerley to leave the historic Kerley holdings in South Carolina. After 1830, there are very few mentions of any Kerleys in South Carolina. Arthur took his family to Montgomery County, Alabama. Apparently that was where his wife's family lived. Arthur shows up there in the 1830 census.
Things apparently did not work out as planned in Alabama because 10 years later Arthur is in Lauderdale County, Mississippi. He is there in the 1840 census. And, that is where he died 10 years later in 1850. Arthur fell on hard times in his later years. He became very poor, had to live with one of his sons, ran a moonshining operation, got arrested for that moonshining, and ended up a ward of the state. The description of these hard times can be found in this series of stories (some of the historical data (i.e. "facts" about Arthur's origins) in these stories is inaccurate, but the anecdotes of his later troubles are credible. http://www.sharpwriters.com/genealogy/kerley.html
John3 (Joseph2,William1). The only reason for putting John as a son of Joseph is that he was born in 1788 in South Carolina. The only known Kerley living in South Carolina at that time who was old enough to father a child was Joseph. John settled in DeKalb County, Alabama. He shows up there in both the 1850 and 1860 censuses.
John served with his brother, Arthur, in the War of 1812. See War of 1812