Green’s Dictionary of Slang

a charge sufficiently serious to be heard at a Quarter Sessions (rather than in a magistrate’s court).

1824

J. Wight Mornings at Bow Street 100: [He] escaped the Sessions, though the assault and outrage he had committed were certainly most sessionable.* [[fn.:] "This is a sessionable assault; that is to say, an assault worthy of trial at Quarter Sessions." — Country Justice].