Green’s Dictionary of Slang

not worth a fuck phr.

also not worth a tuppenny frig
[fuck n. (1a)]

absolutely worthless.

[US]T. Harrison V [poem] ‘Listen, cunt!’ I said, ‘before you start your jeering / the reason why I want this in a book / ’s to give ungrateful cunts like you a hearing!’ / A book, yer stupid cunt, ’s not worth a fuck!
[Ire](con. 1945) S. McAughtry Touch and Go 150: I’m not worth a tuppenny frig.
[US]C. Carr Our Town 283: ‘The judicial system ain’t worth a fuck,’ she concluded.