Pooled in Southern Group D with the Grecians, Bristol Rovers and West Ham Under-21s the green and whites will look to top the group for a third straight season.
Reaching the semi-final stage in 2017/18, Darren Way will once again be looking for an extended run in the competition and will hope for an opening game sense of deja vu.
Town made the short trip to Exeter in the opening group stage fixture last season and came away from St James Park 3-1 victors.
If history is to repeat itself the Glovers will have to cope without Stuart Nelson (calf), Shaun Donnellan (thigh), Tom James (hip flexor), James Bailey (knee), Rhys Browne (hamstring) and Francois Zoko (knee).
Wes McDonald missed the trip to Grimsby but could return in midweek, whilst Jordan Green limped off at Blundell Park and will need further assessment.
Newest recruits Omari Patrick and Fela Olomola could make their bow at home against an Exeter side who’ve made a solid start to the campaign.
Under the new guidance of Matt Taylor the Grecians have 10 points from their opening six matches coming into the cup competition.
Former Glovers Aaron Martin and Nicky Law could well feature for the Devon outfit.
Both sides are tied with five victories each from the 11 previous encounters although momentum sits with Town.
The Glovers are undefeated in their last five outings against City and claimed a 2-0 win last time out at Huish Park.
Jake Gray and Francois Zoko secured the three points with Sam Surridge, Rhys Browne and Otis Khan recording the 3-1 Checkatrade Trophy win last August.
Trevor Kettle will take charge of the midweek match.
In what will be his seventh match of the season, Mr Kettle has so far awarded 19 yellow and one red card.
He’ll be assisted by Samuel Ogles and Christopher Husband with Savvas Yianni acting as fourth official.
A full match report will follow on YTFC.net at full time with post-match reaction from the manager and a member of the playing staff following soon after.