Both units were operating that day and you might want to take a look at my accont at
http://www.ghostbombers.com/SG4/sg4frame.html
III./JG 53 was in action against Spitfires (aborting its escort mission for SG 4's Focke-Wulfs) at 13.23 and 3./JG 4 fought against P-40s at 13.30.