I do not find a James A. Bennett in the 3rd Georgia, however, we have one by the same name with discharge which relates.

James A. Bennett

Residence was not listed;
Enlisted on 4/27/1861 as a 2nd Lieutenant.
On 4/27/1861 he was commissioned into GA Blodget's Light Artillery
He Resigned on 8/13/1861
Sources used by Historical Data Systems, Inc.:
- Roster of Confederate Soldiers of Georgia 1861-1865

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James A. Bennett

Residence was not listed;
Enlisted as a 2nd Lieutenant (date unknown).
"C" Co. GA Blodget's Light Artillery

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This could possibly be your man if the age fits:

James A. Bennett, enlisted in Captain Stovall's Company, Cobb's Legion, Georgia Cavalry (Company A), September 14, 1861, recorded as a 2nd Lieutenant, age 36 on April 3, 1862 at Atlanta, Georgia,