Coosa County belongs to the 3rd Congressional District of Alabama. During this period the 6th Congressional District included Blount, Franklin, Jefferson, Lauderdale, Lawrence, Limestone, Marion, Morgan, Walker and Winston.
"Supporting Forces" is a term applied to companies raised to support operations of the Conscript Bureau. Of course anyone exempt from Confederate service could belong to such a command; a member did not have to be a resident of the 6th Congressional District. You may see references to Supporting Forces as "buttermilk cavalry". A significant part of "Cold Mountain" deals with a company of Supporting Forces led by Capt. Teague in westen North Carolina. If I'm not mistaken, his real name was used in both the novel and the movie.