There does not appear to be any records of Graham's Georgia Battalion. It may have been a local defense unit formed late in the war which would explain there being no records. Many Confederate records from mid 1864 did not survive to be incorporated in the Official Records.

His pension application indicates he joined Graham's command at Athens, Ga. and remained on duty with them to the end of the war when they were located between Macon and Columbus, Ga.

...........

James Leckie

Residence Hall County GA;
Enlisted on 9/10/1861 as a Private.
On 9/10/1861 he mustered into "D" Co. GA 27th Infantry
(date and method of discharge not given)
(No further record in this company)
On 12/15/1864 he mustered into GA Graham's Battn *
(date and method of discharge not given)
(Estimated day of enlistment)
(Born in 1845)

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

* at Athens, Ga. and remained with them to the surrender when they were located between Macon and Columbus, Ga.
Died January 4, 1924
Pension Applications of Confederate Soldiers and Widows
Ancestry.com

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James Leckie, Private, Company D, 27th Regiment Georgia Infantry, enlisted February 23, 1862 in Hall County Georgia by Lt. Kennedy for the duration of the war, receipted for issues of clothing September 20 and in the 4th Quarter, 1864, his file contains a note between the Adjutant General, War Department with the Georgia State Board of Pension Commissioners dated May 26, 1917, no other records

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