The 15th Confederate Cavalry muster rolls are posted on Ancestry. Your soldier is listed as "J H Ballard".

On Ancestry go to search>type in: j h ballard>scroll to military>confederate service records 1861-1865>fifteenth confederate cavalry.

Ballard was in Company E, Private, enlisted at Greenville, AL by S. J. Bolling on 12 May 1862. He was sick in Nov & Dec 1863 and apparently was given furlough. Remarks on his muster card was that he deserted while on furlough in Butler County, Alabama about 1 January 1864.