According to the little I can find, Thomas McAdory (1738 - 1790) came to South Carolina about 1767. His sons were Robert (1770 - 1840), James (1773 - 1815) and Thomas (1776 - 1820). The younger Thomas McAdory followed a common migration pattern, moving from the central Carolina Piedmont country to western Kentucky. Shortly before Alabama became a state, he brought his family to the future site of Birmingham where he died in 1820. His son Thomas came to Jefferson County as a small child, born 1817 in Christian County KY. James McAdory mentioned in earlier posts was the older brother of Thomas (b. 1817) and son of Thomas McAdory (1776 - 1820)
I don't have anything about Thomas McAdory's sons Robert and James, but a McAdory family researcher writing in 1911 mentioned that their descendants migrated to Mississippi. Thomas McAdory's (1776 - 1820) sons became prominent settlers and developers in Jefferson County. Evidently his two brothers have Mississippi connections that you may know about.