Other than 3rd MS State Battn record for the older of the two, no Confederate military records under this name. A U S Pension Application was filed Dec 3, 1920, under the name Josiah Byrd, Co "E", 2nd Miss Regt. Do not know if the application was white or black, or what period of time service was claimed.

Josiah Walton Byrd Jr was quite young (born Feb 10, 1847), so it's entirely possible he never enlisted during the war.