Harry Burke is probably an alias for James P. Johnson.
Nina Simone [as Ginhouse Blues]
Paul Williams & The Big Roll Band [as Gin House]
Animals [idem crediting Henry Troy & Fletcher Henderson who cowrote another Ginhouse Blues, also introduced by Bessie Smith (in '26)]
Amen Corner [idem]
Cuby & The Blizzards [idem]
Big Town Playboys [idem]
The Gin House Blues Bessie Smith recorded in 1926 is a different song, written by Troy/Henderson and opening with the line: "I've got a sad sad story today". Me And My Gin opens with: "Stay away from me 'cause I'm in my sin".