Do you have census information that shows this man's name in Morgan County? After looking at the 1850, 1860 and 1870 census records, I don't see it in any form. The name "McCarley" is much more common, and several families by that name were recorded in Morgan County during those years. There were at least three McCarley boys in Co. "D", Russell's 4th Alabama Cavalry, and another in Co. "K", 9th Ala. Cav. Regt. There's also two McCarley men in Co. "H", 27th Alabama Infantry. These were recruited (at least in part) in Morgan County. Thomas J. McCarley, who was recorded in jail at Somerville AL in 1860, appears in Co. "E", 9th Alabama Cavalry, a Lauderdale County unit.

I didn't see a Joseph in any of the McCarley families, or in the list of Alabama soldiers.