The Me 109F1 had a motor canon.
This is the quartermaster generals report on DB601N engines in service. It also notes the number of Me 109F1 in service.
Bader was shot down over France in August 1941, well after the BoB was over but also by then Me 109 F was in service.
And yes I've heard of Me 109F having the wing guns and the nose gun for a short time. There is a photo with Galland, Goering and an F2 all in it.
On the Generalluftzeugmeister meeting on the 22nd January 1941, the Generalstab pointed out the following figures on the number of 'active' DB 601N installed, referring to reports from the units on 1st of January, thus giving us a good picture on the number of Bf 109E-../N types in frontline service on the 1st of January :
2
in Bf 109s
Bf 109E-1 : 16 pcs, Bf 109E-3 : 1 pc, Bf 109E-4 : 54 pcs, Bf 109E-6 : 1 pc, Bf 109E-7 : 34 pcs, Bf 109E-8 : 2pcs.
Bf 109F-1 : 5 pcs.
Total 112 Bf 109E with DB 601N present in service, plus 5 Bf 109F.
in Bf 110s
Bf 110C-1 : 4 pcs, Bf 110C-4 : 40 pcs, Bf 110C-5 : 12, Bf 110C-7 : 14 pcs, Bf 110D-0 : 18 pcs, Bf 110D-2 : 20 pcs, Bf 110D-3 : 8 pcs, BF 110E-1 : 176 pcs, Bf 110E-2 : 14 pcs.
Total : 306 engines, ie. 153 Bf 110s with DB 601N present in service.
in Misc. types
He 111P : 8 pcs, Do 215 : 68 pcs.
Note how many of these higher powered much higher altitude engines are being "wasted" on Me 110 in an attempt to make it competitive.