Hi, I'm a descendant of Bayless Axton b. 1788 in Kentucky m. to Elizabeth Terry. His father was Isham Axton b. 1761 in England. You can find this on a 1790 census from North Carolina.
My Line:
Bayless Axton, William Levi Axton b. about 1814-19, William Lewis Axton b. 1849 (brother of Douglas), Temple Roy Axton B. 1891 who was my great-grandfather and brother-in-law to Thankful Axton. He lived in Colorado.

I have letter from a descendant of Levi Carter Axton (bother of Bayless) about the Kentucky Axton's if you would like a copy.