[Nokose]

15 Sep 1940 II/JG 2 seems to have been involved in a dogfight with Spitfires possibly in the area of Portsmouth as Hahn's claim gives the only clue with Thorney Island. here is the claims for them.
Fw. Eberhard Bauer 5/JG 2 Spitfire 15:15 no location
Uffz. Karl Hannes 5/JG 2 Spitfire 15:20 no location
Oblt. Hans Hahn 4/JG 2 Spitfire 15:35 Thorney Island

No RAF losses along the southern coast this day and there are plenty of other German units filing claims some with no times and no locations during this time period but all the actual losses seem to be around London and the Thames Estuary. So no actual matching claim for Hahn.