The game against Paul Harsley's former club is set to take place away at the Oakwell, on the week commencing 3 December, with the exact date of the fixture yet to be confirmed.
The Blues finished second in their group, to qualify for the knock-out round, just one point behind Shrewsbury Town following an opening day draw to the group leaders plus consecutive wins over Crewe Alexandra and Tranmere Rovers.
Barnsley finished top of their table with victories over Bradford and Oldham, in addition to a draw against Everton U21s, where the Yorskhire side secured an extra point on penalties.
After booking their place in the next round, Paul Harsley explained the importance of the competition for his developing squad.
"This tournament has been really good for us as we’ve won two and drawn one," the U21 boss told ManCity.com. "It’s the challenge the competition gives to the team – playing on a proper football ground under the lights, the pressure to win a game as well as play well and they did that against Tranmere, but we should’ve won by much more.
"It’s a competition that everyone really enjoys. When we came in after the final match at Tranmere the lads were all cheering.
"I think we’ve done relatively well in the league so far, but obviously the Uefa Youth League has been a bit of a problem for us so far so I think the Checkatrade Trophy is a bit of a release for the players.
"We seem to really thrive in this [competition] and we’ve now got another game in it which gives us something to look forward to as we don’t have to worry about relying on anyone else."
Shrewsbury Town v Walsall
Sunderland v Notts County
Rochdale v Oldham Athletic
Accrington Stanley v Lincoln City
Newcastle United U21 v Macclesfield Town
Mansfield Town v Bury
Port Vale v Stoke City U21
Barnsley v City U21
Chelsea U21 v AFC Wimbledon
Portsmouth v Arsenal U21
Cambridge United v Northampton Town
Exeter City v Peterborough United
Cheltenham Town v Newport County
Luton Town v Southend United
Oxford United v Tottenham Hotspur U21
Swansea City U21 v Bristol Rovers
Checktrade Form 2018/19
Northern Group D...
Shrewsbury Town 1-1 City U21s (Shrewsbury won extra point on penalties)
Crewe Alexandra 1-4 City U21s
Tranmere Rovers 0-1 City U21s
The English Football League Trophy, to give it its official title, was first introduced for the 1983/84 season.
City have played in the competition once, during the 1998/1999 campaign when it was known as the Auto Windscreens Shield.
Joe Royle’s Blues went down 2-1 at home against Mansfield Town, with Danny Allsopp on the scoresheet.
Until the 2016/17 season, only League 1 and League 2 sides had been eligible to compete, but now 16 clubs from the Premier League and Championship that hold Category One academy status are invited to enter an Under-21 side.
Clubs were initially invited based on their 2016/17 league performance and should they not accept, subsequent teams were then offered a place
The introduction of academy teams also saw a change in the competition format, which had previously been a knockout tournament throughout, but now features an initial group stage.
Last season City went out in the group stages, having beaten Rotherham 4-2 on penalties after a 1-1 draw but then losing 2-1 at Bradford before being edged out 4-3 on penalties at Chesterfield after a 2-2 draw in normal time.
Lincoln City were the eventual winners of the Trophy.
Rules to note
•Manager Harsley must name six players in his starting XI who are under the age of 21 as of 30 June 2018. Teams may only include two players on the team sheet, aged over 21, who have made forty or more senior appearances, as at 30 June 2018.
• If scores are level after 90 minutes, the game will go straight to penalties - this will apply up until the semi-finals of the competition.