It appears that during William's lifetime, the family name was in transition as he is sometimes referred to as Abney and other times as Abner. I found this on Find A Grave and also on Ancestry.
Biography
William served in the War of 1812. During the War of 1812 William Abney along with Absalom Troup Abney, Abney Mays, Charles Abney and Thomas Hamilton Abney enlisted in Youngblood's 1st Regiment of South Carollina Militia.
His 1st wife was Delilah Richardson that died around 1818 based on the gap in the childrens estimated ages and his 2nd marriage. His 2nd wife was Elizabeth Graham.
Note
His birth date is estimated from the date of his first marriage and William being 21 years of age. That first marriage has 2 different dates based on sources. The day was the 24th or 25th. Edward Pike is using the later due to Bonds also being used as the Marriage dates.
Marriage 1
William Abney Abney
Event 25 Nov 1813, Estill County, Kentucky, United States
↑ "Kentucky, County Marriages, 1797-1954," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FWRW-FJ5 : accessed 18 July 2018), Reference ID Page 27, Digital Folder 4261073, Image 32, William Abney and Elizabeth Graham, 7 Feb 1819; citing , Estill, Kentucky, United States, Madison County Courthouse, Richmond; FHL microfilm 254,628. Pike-2301 12:25, 18 July 2018 (UTC)
↑ "United States Census, 1820," database with images, FamilySearch, Affiliate Name The U.S. National Archives and Records Administration (NARA) Digital Folder 5156946, Image 52, (https://familysearch.org/ark:/61903/1:1:XHG7-QT9 : accessed 18 July 2018), William Abney, Ravenna, Estill, Kentucky, United States; citing p. 41, NARA microfilm publication M33, (Washington D.C.: National Archives and Records Administration, n.d.), roll 17; FHL microfilm 186,177. Pike-2301 12:25, 18 July 2018 (UTC)
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DNA Connections
It may be possible to confirm family relationships with William by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree:
Abner-208 and Abney-802 appear to represent the same person because: Abney is father's name. Could have changed his name to Abner during course of lifetime. Abner would go in the Current Last Name field. Same find a grave on both profiles. Exact same parents on both profiles.