Jefferson Tankersley was the son of Fountain Tankersley, who married Charity or Chaney Kinney in Clarke County, Georgia on December 13, 1810. That's the only marriage record I've found for him, although in later records his wife is identified as Margaret (she was quite a bit younger than Fountain and seems to have been a second wife). The four children in his estate records were Jefferson; Eliza, who married Robert T. Cowan in 1849; John Milton, born c.1832, who married Catherine L. Weir on April 27, 1858 and died during the Civil War; and Naomi, born c.1835, who married George W. Woodruff in 1856. By 1830 the family was living in Newton County, Georgia, where Fountain died around 1849.
Fountain was the son of John Tankersley and his wife Letty, whose maiden name I don't think anybody knows for sure. John and Letty came to Georgia in 1784 from Henry County, Virginia; you'll find records of this family in Greene, Hancock, Clarke and Morgan counties in Georgia. John died in Morgan County between 1816 and 1818. John and Letty's other known children were William, Carter, Mary, Naomi, Winnie, Rachel and Sarah.
Most researchers, including me, have concluded that John was the son of Richard Tankersley Jr. of Caroline and Amherst counties, in Virginia. There's no evidence as to whether he was the son of Richard's supposed first wife, Elizabeth Fountain, or his apparent second wife, Winnifred (surname also unknown). The fact that John had a son named Fountain and a daughter named Winnie is obviously no help here. Even if he was the son of Elizabeth, however, he would almost certainly have been raised by Winnifred, who had married Richard Jr. by 1849. Incidentally, there's no hard evidence of Richard's reputed first wife, Elizabeth; Winnifred is the only one who ever appears in public records.
Richard Jr., who died around 1797 (not in 1748, as the erroneous old genealogy by Charles W. Tankersley claims), was the son of Richard Tankersley Sr. of Caroline County and his wife Margaret Mathews.