> I found a J.T. Abernathy in Fayette County, TN. for the 1860 US Census. Could this be him with a "T" initial rather than > the presummed "H" initial?
Perhaps. There's not a lot to go on there, save Fanny and "Belger" whom I'd presume was Mary Belzora, the other named daughter I had for the couple. Ann's birth year doesn't match at all well, his is off a tad, too, but that's often the case. Still, I would not claim him as Joseph son of William and Winifred (Kinbrel) Abernathy until I'd taken a look or two over a few Fayette County records: deed indexes, tax records, jury lists, et cetera.
> Do you know who this family belongs to if not him?
No, but I also would not claim it's him just yet. Not on the basis of that one census record. I'd want to locate him on the 1850 one, too, if at all possible. Otherwise, it's too little to go on, and far too easy to make a mistake and thoroughly bollux up everything for researchers yet unborn. Look at all the people that still insist on giving the Robert Abernathy of early Jamestown a middle initial when it is now known that practice only came about because of the space constraints of a small town newspaper column in the 1930's and the saving of seven characters every time "A." appeared instead of "Abernathy", which was very often, indeed!
> I found that Abernathy was spelled Abernathey on the Census often.
I've also seen it as Abaunthey, Abournathy, Abergothy, Abbbenathy, Abbenithy, and a lot of other mangled spellings.