Martha

Corp. A.T. Humphries is listed in the Confederate parole records provided by the National Parks Service's Vicksburg site.
http://www.nps.gov/vick/parole/cp_h.htm

The Mississippi Sons of Confederate Veterans Web Site provides a unit history for the Mississippi Minute Men (State Troops).
(Scroll down to 5th (Robinson’s) Regiment Mississippi Infantry Minute Men)
http://mississippiscv.org/MS_Units/minute_men.htm

For burial sites of your Humphries relatives in Winston County, I would suggest posting a query to the following board for a cemetery look up.