While not them specificly in general were military police.They were brought into fighting at times when needed.Mostly to put down local insurections both civil and military within the area they occupied.Louisville was the main supply depot for both the Armies of Ohio and Cumberland.Some were used as shipping control.Handled POW's forwarded to northern prisons.
They had many duties in 1863 the Fayetteville,Ark.Provost listed his contributions to the war as :Exercising the functions of judge,jury and sheriff;empowered to arrest deserters,all disloyal persons;enquire into and report treasonble practices;sieze stolen or embezzled property belonging to the U.S.government;detect spies of the enemy;put a stop to misc.pillaging...Responsible for the adminstration of bonds and passes both military and civilian, loyalty oaths given....in general, administration of law during the suspencion of civil process(habeas corpus).
To some extent recruiting including enforcement of conscription laws.
Garfield(future Pres.)was head of provost Army of the Cumberland.
While not Federal it worked much the same read: Rebel Watchdog,The Confederate States Army Provost Guard,Kenneth Radly,LSU press
My GGGrandfather was transfered to Provost Duty in Illinois from Army of the Cumberland May 14,1863.Mainly recruiting when he got several(just west of Chicago) he accompanied them to Camp Yates and Butler in midstate for deployment.He was a officer and accompanied details from Camp Douglas to Camp Yates upon occation.I have copy of orders for him to be on the lookout for a deserter headed home from Chickamaunga.He became a policeman after the war, for a time, most likely because of his provost training.Provost were not well liked by anyone civilian or military and many of the officers were considered substandard to fighting men in the field.They would of had their hands full in Louisville.States had there own as well as the armies.Those operated under state A.G. check state records.Good Luck!