Abner Hammond is listed on the 1790 Edgefield County, SC Census:
Hammond, Abner 1 0 0 0 0
The RSCP lists Abner's birthday as 25 JAN 1762. Further ths book lists Leroy as an uncle to Abner and that Abner served under both Samuel and Leroy in the Revolution. It would seem unlikely to me that Abner would serve under Samuel if he were older, especially since Samuel was quite young himself. On the other hand, the birth and baptism record cited above are considered more accurate. The RSCP also lists Abner as Abner, Sr. We may have 3 men named Abner here.
REF: IGI Batch #: 7717101, Sheet #: 42, Source Call #: 1059267
IGI Batch #: 6932861, Sheet #: 31, Source Call #: 538163
Letter in the Augusta College Library from Jacob Rauers, 1721 Cloverdale Ave., Baton Rouge, LA 70608, dated 7 NOV 1973.
Roster of South Carolina Patriots in the American Revolution. p. 407.