I am James Abernathy/ Artimesia Smith - John Washington Abernathy/ Caroline Ware descendent.I may be able to help find some contemporary male Abernathy's for DNA testing for you.
My grandfather, Hugh Collins Abernathy, was the son of John Washington Abernathy.Hia son, John Pierce Abernathy, Tuscaloosawas my uncle.(sorry, don't know dates but JP and his sisters were all born circa 19-teens), who had two sons, John and Hugh.
I'm considerably younger than Johnny and Hugh and have lost track of them over the years, but last I heard, Hugh was still in Tuscaloosa and Johnny in Birmingham.They would be in their 70's, maybe even 80's, if they are still alive.
I know that Johnny did not have a biological son.Not sure about Hugh but don't think he did either.
Not sure this is of much help.My older sister is searching through her house, looking for an addresses.However there may be enough information here for someone closer to the source to locate them.