This may be him.

Arthur C. McCoy, Private, Company A, 1st Regiment Missouri Cavalry,* enlisted July 1, 1862 at Duval Bluff by Capt. Shelby , subsequently commissioned 1st Lieutenant January 11, 1863, on detached service “to pick up deserters,” February 5, 1864, captured near Arkansas Post February 6, 1864, confined at Little Rock, Ark. February 17, forwarded to Rock Island, Ill. prison June 23, 1864, paroled in 1865, no date recorded, born in Virginia

* This regiment was subsequently designated as the 5th Regiment Missouri Cavalry

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Missouri