Nor is there a roster found in the National Archives Compiled Service Records transcribed by Fold3.com.

4th Regiment Indian Home Guard
Organization commenced but not completed. Men transferred to other organizations.

…

Understand that some of these men of the Indian Home Guard, Regiment 1-3 previously had service in the Confederate army.

I found this man with the same name, and present for your information.

William Browning, Private, Company C, Deneale’s Regiment Choctaw Warriors, enlisted January 14, 1862 at Doaksville, paid $50 bounty July 14, 1862 at Richmond, signed with an ‘X’, his mark, no other records

Deneale’s Regiment Choctaw Warriors (also known as Deneale’s Confederate Volunteers) was organized as a battalion by authority of the Secretary of War dated December 14, 1861. The battalion was temporarily disbanded about May 5, 1862, but it appears to have subsequently been reformed and reported as a regiment

It is interesting to note that all four officers of his Company C signed for their bounties with an ‘X’!

M258: Compiled Service Records of Confederate Soldiers Who Served in Organizations Raised Directly by the Confederate Government.