Which city in South Yorkshire was ceded to the Kingdom of Scotland in the first Treaty of Durham of 1136, a move that was never formally reversed?

Doncaster. David I of Scotland invaded and took several cities and territories and the Treaty of Durham established a peace which saw David I retain some of the property claimed including Doncaster.

https://en.wikipedia.org/wiki/Treaty_of_Durham_(1136)

To add to the information given above:

The first treaty of Durham was a peace treaty arranged between King Stephen of England and King David I of Scotland in February 1136.

To prevent further military invasions, David was ceded Doncaster as well as small parts of Cumberland and Lancashire. His son and heir, Prince Henry of Scotland, formalised making Doncaster a Scottish borough.

Henry II, who succeeded King Stephen, regained control of Doncaster in 1157 but there is doubt Doncaster was officially returned to England or if it technically remains Scottish because of no formal handover.

Thise ambiguity about Doncaster's status caused Doncaster City FC to make an ultimately unsuccessful 2022 bid to join the Scottish Cup, based on the 1136 treaty.

https://www.itv.com/news/calendar/2022-09-22/english-football-club-bids-to-play-in-scottish-cup-under-1136-treaty
https://www.bbc.com/travel/article/20211019-the-scottish-town-stranded-in-england