I'm not sure that Rufus S. Adair belongs as one of the children of James and Ann Smith Adair.It's known that James and Ann had the two sons -- John Smith Adair b. 1822 and Andrew Jackson Adair b. 1831 -- and possibly a daughter, Jane.John Smith Adair married Mary Ann Heslep and they had a son named Rufus Heslep Adair.
(Note that John Smith Adair is also claimed by some members of the Whitmill Harrington Adair family of Paulding County, GA as one of Whitmill's children.)
Both J. S. Adair and A. J. Adair were in the 1880 census of Tate County, Mississippi, listing their birthplace as GA, both parents born SC.My ancestress Jane Adair Brooks, who may or may not be the "Jane Adair" sister of these two brothers, was in the 1880 census of Frio County, TX as born in GA, both parents born GA.
I have been researching these Adair families for over 30 years and find it almost impossible to untangle them.