Taumahill, William M. (also on Rolls as Tannehill, W. N.), Pvt. Co. C, 3rd La. Inf. Federal Rolls of Prisoners of War, Captured Snyder's Bluff, May 19, 1863. Sent to Memphis, Tenn., May 25, 1863. Recd. Fort Delaware, Del., June 15, 1863. Transfd. from Fort Delaware, Del., to City Pt., Va., for exchange, July -, 1863, Died Fort Delaware, Del., Aug. 16, 1863.
The POW camps, in some instances, have good records as to where and when captured. You might want to google the camp organization, and see what they have