First, I am reasonably sure that I have located Smith Abernathy or Abernethy on the 1790, & 1800 Lincoln County NC census records, on the 1810 Rutherford County NC records and is probably the Smith Abernathy with family on the 1820 Lincoln County, TN records (self & wife, three younger males and 6 younger females in the household). I find that he stood surety for the marriage bond of John Rockett to Sarah Abernathy 11 Jan 1787 in Lincoln County NC [Curtis Bynum's "Marriage Bonds of Tryon and Lincoln Counties, North Carolina", Catawba County Historical Association, Inc Newton, NC (1929), p. 107, bondsman Absalom Spencer].
The census records, although not what we'd have prefered, do certify that he and his wife (sorry, I have no given or maiden name for her at all) had at least 7 children, and I think I may have identified all of them.
Eldest son Robert was b cir 1785 and I show him married on 23 Feb 1811 to a Polly Payne in Burke County NC; the couple are on the 1850 Lincoln County NC census, but I do not know of any children from this marriage. Next, daughter Susana, who married 5 Sep 1805 in Lincoln County NC to Richard Johnston [Bynum, op. cit., p. 71, bondsman James Johnson or Johnston]. Again I have no record of children. Third, Martha B. Abernathy who, according to Sharyn Young's 6 Jun 2005 online tree on ancestry, married John Carson Gettys on 9 Nov 1809, which I've yet to personally document. I list 10 children from this marriage, but can only verify three of them via the 1850 Rutherford County NC census. The names I have for these children are: Nancy, Elizabeth, James (middle name Abernathy), Alexander, John Carson (Jr), Martha, Smith, William, Mary, and Robert. I have spouses for Elizabeth, James, Alex, John, and Smith, but haven't really researched them thoroughly. The 2nd son, Alexander, married and remained in Burke County as a Baptist Clergyman. He's found on the 1820, 1830, 1840, 1850, and 1860 census records. I have brought some of Alex & Elizabeth Wilkie's issue forward to the present day. I show that daughter Sarah married Thomas Parker 22 Feb 1814 in Rutherford County NC [Rutherford Co, NC Marriage Bonds, bondsman John Parker]. Daughter Elizabeth "Betsy" married Thomas Brown 6 Nov 1815 in Rutherford County NC [Rutherford Co, NC Marriage Bonds, bondsman (again) John Parker]. Possibly both daughters, their husbands, and young children were part of that 1820 household of Smith Abernathy in Lincoln County TN (p. 255). Lastly, I have son Smith (Jr.) who married Carolina Jones abt 1842 and is fornd on the 1850 Catawba County NC census record.
Finally, I have this individual in my database as a son of the 4th Robert Abernethy (1719 VA - 1798 NC) and his wife Sarah (nee Abernethy). This Robert moved into Granville County NC in 1752. From 1754 to 1769 he was a Lieutenant then Captain in the NC Militia company of Captain Richard Coleman.
The 4th Robert had 7 sons and at least 2 daughters, one of whom, Amy, married Absolum Spencer 19 Jan 1809 in Lincoln County NC [Bynum, op. cit., p. 119].
This Robert, of course, was a son of the 3rd Robert, whose will was signed 31 Jan 1772 in Lincoln County NC. Despite the many online databases to the contrary, we still have no idea what so ever concerning the maiden name of his wife, Mary. The 3rd Robert's parents were Robert (2nd) and Christian Parham, and his parents were Robert (1st) and Sara Cubisha.
While I do not have a will or deed record that explicitly links Martha (Abernathy) Gettys with her father, Smith, I have little doubt that the circumstantial evidence we have in hand is probably reasonably sufficient to substantiate the link.
And there you have the gist of what I have on this Smith Abernathy. Except that I cannot find him or his family anywhere in TN or elsewhere after 1820.