I'm not really an Abernathy researcher.Just thought I'd pass this along.Source: "A Biographical Souvenir of Texas", F.C. Battey & Co, Chicago, 1889 (that's right -- 1889).
I will paraphrase.
#1: Jesse Abernathy was a veteran of the American Revolution, and later served in the Tennessee legislature.
Son, Richard Abernathy born c1801 and died 1851.Married Alice Tarpley born c1800 and died 1842.
Son, Frank J. Abernathy born Feb 17, 1837, Giles Co, TN.Educated Giles College, Pulaski, TN.Moved to Dallas Co, TX 1862.Moved to Fannin Co, TX 1867. Became Real Estate and Loan Broker.(Possibly still unmarried at time of publication in 1889.)
#2: David Abernathy born c1810 Lincoln Co, North Carolina.Married Frances Franklin born c1825 North Carolina (she was still living 1889.Moved to Mississippi 1849.Moved to Collin Co, TX 1886.Died there.He was a farmer and Methodist Episcopalian and fathered nine children.
Son, Mercer G. Abernathy born Apr 20, 1854, Marshall Co, Mississippi (6th child of David and Frances).Moved to McKinney, Collin Co, TX 1876 and became a Lawyer.Married Nov 20, 1880 Bell Forman of Plano, TX.Nov 1888, elected County Judge of Collin County.As of 1889, three children: Donna, Ethel, and an as yet un-named infant.