Here, I believe is your man.
You now need to obtain his service record file which can be achieved through a service noted at the top of this page.
George Martin
George W. Childers
Residence was not listed;
Enlisted on 3/28/1863 at Buchanan County, VA as a Corporal.
On 3/28/1863 he mustered into "G" Co. KY 14th Cavalry
(date and method of discharge not given)