There is a record in Halifax County of David Adkisson Sr selling 61 acres purchased from his father Wiiliam Sr to John Adkisson. It was not clear to me if this was David's son or as you suggest William's son.
Then there are 2 documents that relate to the fact that Louisa is his daughter 1835 Apr Court Minutes Book Tipton County, Tennessee, USA Court minutes from 4-1835 appoint John Adkinson Jr and Benjamin Stokes Administrators of the estate of John Adkinson Sr. Page 96 of the Tipton County Court minutes. Now this gives his dob about 1780
Guardianship of Younger Siblings Tipton County, Tennessee, USA p. 172 of Tipton County Court Minutes Book for June Court order John Adkinson be appointed Guardian for minor children David and Louisa Adkinson, minor children of deceased John Adkinson.