This could be him:

Jacob D. Conner [Jr.], 2nd Lieutenant, Capt. Joseph Bledsoe’s Company, Artillery, Shelby’s Brigade, Missouri, Cavalry, enlisted June 30, 1862 at Duval Blf., Ark. by Col. Shelby for the war, commissioned September 20, 1862, absent on detached service February 24, 1863, received pay August 1, 1863, no further records

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