There is only one A. Martin on the roster of the 38th Georgia.

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Absalom C. Martin

Residence Dawson County GA;
Enlisted on 5/6/1862 as a Private.
On 5/6/1862 he mustered into "I" Co. GA 38th Infantry
He was Surrendered on 4/9/1865 at Appomattox Court House, VA
He was listed as:
* Wounded 9/19/1864 Winchester, VA
Promotions:
* 2nd Corpl (1864)

Sources used by Historical Data Systems, Inc.:
- Roster of Confederate Soldiers of Georgia 1861-1865
- Southern Historical Society Papers: Appomattox Paroles ANV

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Abslom [sic]/Abner Martin, Private, (Old) Company N, 38th Georgia Infantry (Wright Legion),* enlisted May 15, 1862 at Atlanta, Ga. by Capt. Blackburn for 3 years, absent sick in hospital October 31, 1862, at home on sick furlough at the end of year, paid January 2, 1863 for commutation while on sick furlough October 13, 1862 to February 8, 1863, wounded near Winchester, Va. June 13/14, 1863, attached as Nurse June 23, 1863 at Jordan’s Springs, Va., recorded present August 11, 1863, listed as 2nd Corporal September 12, 1864, receipted for issues of clothing Sep. 28, Oct. 3, Dec. 13, 1864, surrendered and paroled at Appomattox Court House, Va. April 9, 1865, description: 34 year old Farmer,, 6’ 2”, fair complexion, blue eyes, dark hair, born in Dawson County, Ga.

* This Company subsequently became (New) Company I, 38th Regiment Georgia Infantry

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