Stockdill, 24, moved to Ossett Albion from Hyde United in January 2018 and then stayed with the merged club that summer.
Staying alongside the central midfielder is the club’s record goal scorer, Tom Greaves, who will also join the coaching staff.
Midfielders Elliot Harrison and Aaron Haswell, defender Ross Hardaker, forward Nick Guest and recent signing Eddie Busfield have all agreed deals for the 2020/21 season.
Leaving Ingfield is James Knowles and Marko Basic, who will be joining a club closer to where he attends university.
Meanwhile, the club revealed last month that the future of Ingfield is safe following the public legal matter and court case it was involved in.
A deal has been done to pay damages and the outstanding legal fees, thanks to low interest loans from people associated with the club, who wish to remain anonymous.