I found a Anderson Harris (Below)in the CWS&S at
http://www.itd.nps.gov/cwss/soldiers.cfm Of cource there are several "A" Harris listings

Anderson Harris (First_Last)
Regiment Name 37 Tennessee Infantry. (7 Tenn. Reg't Prov'l Army. 1 E. Tenn. Rifle Regiment.)
Side Confederate
Company G
Soldier's Rank_In Private
Soldier's Rank_Out Private

I found a Anderson M. under Confederate troops I don't think that is your ancestor.

George