Roster of Confederate Soldiers, 1861-1865 shows:

Cauthron, Wiley AR 15th (N.W.) Inf. Co.B

Compendium of the Confederate Armies - FL & AR by Stewart Sifakis, pages 99-101 & 69

ARKANSAS 15TH NORTHWEST [HOBBS'-BOONE'S] INFANTRY REGIMENT
Organized by the change of designation of the 21st [McRae's] Inf Reg ca. Feb 1863 - Reg surrendered at Vicksburg, MS 7/4/1863 - paroled later in month - consolidated with 14th, 16th, and 21st Inf reg's & designated 1st Inf Reg Consolidated in Jan 1864.
BATTLES:
Vicksburg Campaign - May-July 1863
Grand Gulf - 4/29/1863
Port Gibson - 5/31/1863
Champion hill - 5/16/1863
Big Black River Bridge - 5/17/1863
Vicksburg Siege - May-July 1863

ARKANSAS 1ST Inf Reg Cons
Organized by the consolidation of the 1st, 2nd, 5th, 8th, 13th, 15th, 19th [Dawson's] and 24th Inf Reg's and 3rd Inf Reg at Smithfield, NC 4/9/1865 - surrendered by Gen Joseph E. Johnston at Durham Station, NC 4/26/1865
BATTLE: Carolinas Campaign - Feb-April 1865