Joseph Adkins and Daniel Adkins migrated to Georgia from Petersburg, VA. Joseph and his wife Anne Harris Adkins settled in Washington County. Daniel and his wife Penelope Tyson Adkins settled in Warren County. Aaron and Penelope Adkins had several children: John, Aaron, Amacy, Elizabeth, Nancy, Alcy, Sarah, Mary(Polly), Penelope II(b. 1812) and Joseph.
I do know that Joseph and Anne Harris Adkins of Washington County had several children as well. But the only one I'm sure of is John Adkins. John Adkins married Penelope Adkins II (his first cousin) from Warren County. They had several children: Frances, Sarah, Catherine, Daniel J., John S and William J. They lived in Washington County.
I did discover that the brothers Daniel Adkins and Joseph Adkins were originally born in Williamsburg, VA before migrating to Petersburg and then to Georgia.
Daniel Adkins was born in 1767. Joseph Adkins was born circa 1770.
I'm not sure if your William Adkins is an ancestor of these two brothers, or a descendent.