Here's a start for you.

Go to this link: http://www.nps.gov/vick/al/al_lst.htm
for a list of the Alabama units involved in the Siege of Vicksburg.

Then, correlate those to the Alabama unit histories at Dr. Ken Jones' website: http://www.tarleton.edu/~kjones/alregts.html

It should soon become apparant which unit/s fit your battle list.