These are the closest I could locate:

A. A. Harrison
Enlisted as a Private
"C" Co. TX 17th Infantry

.........

Absalom Clinton Harrison
Enlisted as a Corporal
Promotions:
* Qtr Master
"A" Co. TX 18th Infantry
Other Information:
born 12/10/1841 in Perry County, AL
died 7/8/1924 in Alto, TX
(Son of Samuel T. and Ann White Harrison)

Sources used by Historical Data Systems, Inc.:
- Index to Compiled Confederate Military Service Records
- Confederate Veteran Magazine [XXXIII, p. 26]

.....

Absalom Harris

Residence Troup County GA;
Enlisted on 7/8/1861 as a Private.
On 7/8/1861 he mustered into "K" Co. GA 13th Infantry
(date and method of discharge not given)
He was listed as:
* Paroled 9/29/1862 Shepherdstown, VA (No further record)

Sources used by Historical Data Systems, Inc.:
- Roster of Confederate Soldiers of Georgia 1861-1865