What's the shortest amount of time a commercial airplane will be on the ground in between flights?
I flew SA-226/227 Metroliners for two different commuters back in the 1980s. If we were behind schedule, station managers had the option of asking the pilots to do an engine-running turn. The passenger entry door and the cargo door were on the left side of the airplane, so that meant the right engine was left running.

Such turns, usually only requested if there were few passengers exiting and entering, and little baggage being unloaded and loaded, took as I remember less than 10 minutes. The Metroliner was very noisy even with only one engine running and you didn't want to do it if any kind of a line would form at the bottom of the entry stairs.

Captains had the option of refusing such turns, and some captains wouldn't do them.