The correct answer is Leicester!
Between Gameweek 36 and Gameweek 38, the Foxes featured five players in the Kings of the Gameweek teams, more than any other club.
Gameweek 37 - Harvey Barnes, James Maddison, Jamie Vardy
Gameweek 38 - James Maddison, Ayoze Perez
Brighton, Everton and Man City players all featured three times.