Considering the Allied numerical advantage the Luftwaffe would have been mostly doing counter air interdiction. I.e. trying to prevent Allied fighter-bombers from doing their job. Supporting ground forces also means protecting them, not just shooting at the other guys.
However they did that too. I quote from "Luftwaffe over Arnhem":
"During the Battle of Arnhem/Oosterbeek the Germans were able to effectively request air support through the Luftwaffe Liaison officers located within the IInd SS Pz Kps HQs during the whole operational period. The Liaison officers requested air support not only for engaging allied transports over the drop zones but also for air cover for German troop movements as well as strafing runs on known British strong points. Of course the Luftwaffe did not always hit the right target on the ground and the Germans did suffer casualties from their own planes during the operation.
During the period 17th – 26th September 1944, the Luftwaffe employed up to 10 different Jagdgeschwaders that flew from airfields such as Dortmund, Werl, Paderborn, Guetersloh, Stoermede, Achmer, Lippspringe and Plantluenne. They were to score a total of 122 victories over this period with more than half of them coming from JG 11 and JG 26 combined. It was these two units during September 1944 that housed the famous Luftwaffe Aces or ‘Experten' such as Priller, Grislawski, Mietusch and Krupinski."