Another challenging question. Having reviewed the internet, my personal copy of 'Encyclopedia of Western Gunfighter', and the List of Old West gunfighters maintained by Wikipedia, I came up with only two candidates that could potentially qualify. Future Deputy Marshal Heck Thomas was in Rome, GA, in 1863, which would have put him just northwest of Atlanta - prime area for conflict, but he would have been 14 yoa during the Battle for Atlanta, and this is too old to fit. The only other "gunfighter" I can find that would have been 13 years old, and living in Georgia (Valdosta) during the Battle for Atlanta is Doc Holliday. Neither of these two appear on Georgia Militia rolls (and being way underaged, that's understandable) and I can find no reference to either being in, or serving with, the militia. Heck had actually just returned to Georgia after serving with his father and uncle as a courier with the 35th Georgia Infantry.
I am going to guess Doc Holliday is the answer, but only because he fits "most' of the OP's description, was the only 13 year old during the described period, but I can find no reference to him serving in the state militia.
The bonus is
Major Pauline Cushman