Well if you want to get really picky, the original Captain of the Enterprise
was Robert April from 2245-2250(ish). He was established in a TAS episode.
However there is only one Captain who was known as James T so assume that the question refers to that individual.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)