Grace Hollis Puryear shows your William Puryear to be a son of John Alexander Puryear born about 1776. Do you feel that this is not correct?
I show your great grandfather James Granderson Puryear (born 11/30/1837) to be a son of Seymour and Harriett Sage Puryear. The family is in the 1850 census for Randolph County, Arkansas with Seymore Preyear as the head.
I do not know who is the father of this Seymour Puryear but I have long felt that he is a son or a nephew of John Alexander Puryear.