Surnames starting with A & B are found on the roll of the 35th Infantry with 37 A's and 154 B's

However, the only Ball listed is

Jonathan Ball, Private, Company I, 36th Alabama Infantry, enlisted August 8, 1862 at Mobile by Capt. Calvert for the war, attached to the General Hospital Ross, Mobile, Ala. as a Nurse February 13, 1863 and noted left March 25, 1863, last recorded as having receipted for an issue of clothing, 2nd Quarter, 1864, signing with an 'X', his mark, no further records

M311: Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Alabama

Roll 362 35th Infantry
A-P
Roll 363 R-Y
36th Infantry
A-B