With the usual caveats applying on using Wikipedia as a source, their page on the PLAAF Airborne Corps lists a formation of nominally airborne troops, dubbed the 15th Corps, seeing combat in Korea from 1951, and I think I remember that notion from a book on Korea many years ago, but I might be misremembering.
https://en.wikipedia.org/wiki/People%27s_Liberation_Army_Air_Force_Airborne_Corps
I hazard the guess, though, that given UN air superiority over most of the peninsula for most of the war, they were never actually used in airborne operations (or were plans for such ops considered), much like the German airborne troops after Crete.
As for North Korea, I doubt that they were in a position (logistically and organisationally) to actually field airborne troops as early as 1950-53.
I think that article suggests that the PLA Airborne traces its '
lineage' to a formation existant at the time of the Korean War. They didn't become even remotely airborne for another decade.
At the start of the 1950s the PLA, like the North Koreans, would have lacked the transport necessary to drop anything more than penny packets of troops, even if they had wished to.
Interestingly the North Koreans have used paratroopers
since the Korean War but as small commando teams infiltrating the south. The wonderful old Antonov An-2 biplane, being the transport of choice.
Fairly certain that the only sizeable parachute operations during the war were the landings made by the US 187th RCT.