When one does find parent ID, it is on lawyer affidavits regarding claims for the pay & allowances of deceased soldiers.
Your best bet is to check the 1860 or earlier Federal census.
George Martin
J. M. Wilson enlisted as a Private in Company F, Moorman's 24th Mississippi Battalion of Cavalry July 1, 1864 in Jefferson County Mississippi, he was recorded present on his companies Sep/Oct, 1864 muster roll, no further records