The game will be played at Park Hall on Tuesday October 26, with the return leg at the Citizens' Farrar Road stadium a fortnight later, November 9.
The sides last met in the competition group stages last season, when TNS won 5-2 at Park Hall and 2-0 away in Bangor.
The Saints also beat City 2-0 in the final two seasons ago.
In the other semi-final tie, Aberystwyth host Llanelli first, playing the second leg at Stebonheath Park, on the same dates.