Yes, Grace Hollis Puryear has William to be the son of John Alexander Puryear, but she said in her book that it was speculation based on similar names of William and Mary's son's and names in John's family.Nothing more. She thought that William might be one of John's sons that's whereabouts wasn't known at his John's death.
The only other name that I have come up with in connection with Seymore of Randolph Co AR is a James Puryear that borrowed money from Seymore in 1830 and did pay the debt shortly afterwards. The note and receipt are included in Seymores estate papers of 1850.I've never found any other knowledge of this James Puryear.But, I assume it was a brother or I guess it could have been his father, but likely not.My grandfather was only 7 when his father, James Granderson Puryear died.So, I don't think he knew much about his ancestors.All my mother knew was that all the Puryear cousins in Hays and Travis County were distant cousins to us.
After the Civil War, where James Granderson was a prisoner in Indianopoliis, he moved to Christian Co MO.I don't know what took him there.But, he married Mary Wilson Inmon there.They moved to Hays Co sometime after 1876 where Mary and the kids were on an 1876 Mo census and the 1880 census.James Granderson was not listed with Mary in 1876.He may have made a trip down to Texas or more than likely to Randolph Co AR to visit sisters.There was also a civil suit pending in Randolph Co concerning his fathers land.