I could find only these five possible occurrences for Aug 6, 1944.
1) Bf 109G-6 WNr 166010 Stkz KW+YJ "Schwarze (Black) 21 + I"
FhjFw Rudolf Helmut Schindler, unit: 8/JG-53, (not JG 3 or 300).
KIA (killed) 6 August, 1944 during aerial combat with a P-51 near Bleckede about 70 km south east of Hamburg. Reported to have been shot in his chute. Buried in Lüneburg.
2) Bf 109G-6 WNr 165861 Stkz BS+EC "Gelbe (yellow) 7 + I"
Uffz Wilhelm Holtfretter, unit: 9./JG 53.
WIA (wounded) 6 August, 1944 during aerial combat with a P-51 near Bleckede. Belly landed.
3) Bf 109G-6 WNr 441604 "Gelbe (yellow) 14 + I"
Ltn Rudolf Krau, unit 9./JG 53.
WIA (wounded)6 August, 1944 during aerial combat with a P-51, crash landed near Itzehoe about 60 km north west of Hamburg.
4) Bf 109G-6 WNr 165546 "Schwarze (black) 17 + I"
Uffz Karl Passgang, unit 8/JG-53
KIA (killed) 6 August, 1944 during aerial combat with a P-51 in the Braunschweig area, about 200 km south of Hamburg.
5) Bf 109G-6 WNr 440728 "
<<+
Maj Gerhard 'Gerd' Schöpfel, commander of JG 4.
WIA (wounded) on 6 August, 1944 near Schwerin. Bailed out but wounded.
8 and 9./JG 53 at that date were based at Hustedt, about 100 km south of Hamburg.
2./JG 4 was based at Salzwedel ab. 100 km south east and 3./JG 4 at Rotenburg ab. 80 km south west of Hamburg.
Regarding the possibility, instead, that an aircraft belonging to JG 3 and JG 300 could be present in Hamburg area on August 6th, it must be said that:
JG 3 in that period was based: the Stab at Dreux (France), the 1st Gruppe at Burg (near Magdeburg) about 280 km south east of Hamburg.
The 2nd Gruppe was at Nogent-le-Roi (France), the 3rd Gruppe was near Chartres (France) and 4th Gruppe was at Schongau (Germany) but flew Focke Wulf 190s.
JG 300 in August was based: The Stab and the 1st Gruppe at Bad Wörishofen near Munich, the 2nd Gruppe flew Focke Wulf 190s, the 3rd Gruppe was at Jüterbog near Berlin and the 4th was at Reinsdorf (near Berlin).
In summary, considering the distances of the JG 3 and JG 300 bases from Hamburg it is extremely unlikely that any aircraft of one of these units were in the Hamburg area on August 6, 1944.
Notee: Data found in -
Kracker Luftwaffe Archive, in
The Luftwaffe, 1933-45 and in my archives