My GGrandfather was in this unit. some of the battles they were in was fort donalson, Chickasaw bayou that was at vicksburg ms, Port hudson in la, Ramond ms that is just some of the battles i know there were more, There is a book (Holding the line) by Flavel Barber that is a roster record of events he was a officer in the 3rd tn inf,. this is a very good book about the 3rd it will help you greatly.
Johnny Lee