He was an "alternate", i.e., substitute for another soldier.

John F. Conley, age 36, Private, Capt. Helvenstein’s Company, 23rd Battalion Georgia Dragoons,* joined for duty and enrolled January 1, 1863 at Dalton, Ga., by Lt. Col. Avery for the war, discharged by substituting Harrison E. Hamilton, no date, no further information

* This company subsequently became Company F, 12th Regiment Georgia Cavalry

……….

Harrison E. Hamilton, age 49, Private, Capt. Helvenstein’s Company, 23rd Battalion Georgia Dragoons,* joined for duty and enrolled January 1, 1863 at Dalton, Ga., by Lt. Col. Avery for the war, mustered as substitute for John F. Conley, left sick at Ressacca Ga. September 1, 1863 remaining so through the end of year, dropped in obedience to orders for continued absence without leave April 19, 1864

M266: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Georgia