Marsh has joined on a month's youth loan and could be in contention to feature this weekend for their Conference trip to Woking.
Although the transfer window is closed for league clubs, non-league sides are still able to make loan signings.
Marsh, who signed a contract extension for this season, has featured three times in League One for the Reds in 2023-24 and has scored in both his cup appearances, in the League Cup and Football League Trophy.
Earlier in his career he impressed enough to be called into an England under-17s training camp.
In total he has made 16 appearances for his hometown club.
Marsh has a loan spell at Scunthorpe United – then also in the Conference – last term, only for a broken foot to cut it short three games in.
He is the second player to leave Barnsley on loan in the day after striker Aaron Iseka Leya made a temporary move to Israel.
The Minstermen are in the Conference relegation zone but took four points from Ardley's first two matches until defeat at managerless Oldham Athletic at the weekend.