The Glovers will find out who they will play after County and Stanley's replay on Tuesday 18th November after the two clubs drew 0-0 at the weekend.
The second round fixture will be played the weekend beginning Friday 5th December.
Manager Gary Johnson said: "We have some important league games including a game against Notts County on November 22nd, who could potentially be our opponents, however the replay is at Accrington so we will have to wait and see who the victors are from the replay. I will let you know if it is a good draw if we win!"
Full ticket details will be released on ytfc.net in due course.