A brief search shows no one named Lang in the 31st Mississippi Infantry Regiment.
I am not familiar with a 31st Mississippi Militia.

There is a 17 page file on a Clement D. Lang in or near Shubuta, Ms.
He is a citizen, not a soldier and his file is a record of his furnishing goods and/or materials to the Confederate army, for which he was paid. There will only be approx, 8 actual documents, as most have a 1 page cover sheet and a 1 page actual document with the (sometimes brief) details.

As a researcher I have read hundreds of these files. Some have little interesting information and some have lots of it. The way I see it, every little bit data I can find concerning someone I am researching is important.

Ms. Holden,
I can get you free digital copies of this folder if you wish