In the military usage of the time, what we now refer to as the Military Police was called the Provost Guard. The Provost Guard operated under the direction of a Provost Marshal. They were mostly temporary details from the line infantry, but there were some companies which were organized as Provost Guard companies, and that's all they did.

There were two Provost Guard companies in Arkansas that I know of, one each at the posts of Little Rock and Fort Smith.

There's a good book that deals exclusively with the Confederate Provost Guard -- "Rebel Watchdog: The Confederate States Army Provost Guard," by Kenneth Radley [LSU Press, 1989]. A very informative book about a subject seldom written about.