Eugene Randolph Abernathy of Perry, later Madison County MO was one of 9 children of Sidney Abernathy and Virginia Wimsett. Sidney was one of 10 children of James Abernathy and Frances Abernathy. James was one of 9 children of a David Abernathy who died in NC in 1796, after having fought with the British in the Revolutionary War. In his will, this David Abernathy left his son James his "gun", which son Sidney inherited. As I understand it, that weapon was manufactured in England in 1770, and is now in a museum in Oklahoma. James' wife, Frances, was a daughter of Jones Abernathy and Elizabeth Rutledge. After David Abernathy (the Tory) died in 1796, his widow reared the children in Lincoln County NC at least until 1810 when daughter Sarah married Peter Rudolph Conrad there. I believe that somewhere around 1817 Sarah and Peter Conrad and probably most of Sarah's siblings migrated to Missouri, except for her brothers Turner and Grief, who remained in Lincoln County NC. Her brother Joshua married another daughter of Jones Abernathy and Elizabeth Rutledge and had at least 8 children.
In 1824 Grief was bondsman for the marriage of Alfred Abernathy to Magdalene Friday in Lincoln County NC, but it is very doubtful indeed if he was related to Alfred. After that, I've lost track of Grief. Turner, on the other hand had married Susanna Gooding in 1813 and is found on the 1850 Lincoln County NC census, aged 62, as a Miller. Turner's will is dated 24 May 1858 and cites wife Susan, daughter "Siney" (wife of Franklin Oats), daughter Frances Eve (widow of Richard Crow Dec'd), daughter Martha Rebecca, and daughter Nancy Williams "now a single woman". The will was proved in the Jan 1860 court session of Lincoln County. Fanny and Richard Crow had moved their family to MO before 1850, and after 1860 the rest of Turner's daughters did likewise. I believe Nancy died in Texas, but am not sure.
The burial location of James' parents is unknown, but both James and his wife Frances are buried in the York Chapel Cemetery, Longtown, Perry Co, MO, as is son Sidney. I do not know where Virginia Wimsett Abernathy is buried, only that she died after 1880.
I can tell you almost nothing about Eugene R. Abernathy that cannot be learned from the 1920 Madison County MO census records.
There is a tradition among some of this David Abernathy's descendants that his wife's name was Christina Forney, daughter of Jacob Forney and Mariah Bergner. This tradition is, however, utterly false because (among other evidence) the 1804 will of Jacob Forney makes it quite clear that both were alive and well when Jacob signed his will, so Christina Forney's husband David Abernathy (Jr) could not possibly be the David who died in 1796, whatever any of that Missouri family would like to believe. David Abernathy (Jr) was also clearly mentioned in the 1808 will of his father, David Abernathy (Sr). Christina (Forney) Abernathy did not die until 1842, outliving her husband by 4 years. Both are buried in Giles County TN near the home farm they established about 1809 after arriving in TN after leaving NC.