Green’s Dictionary of Slang

worth a... phr.

listed below are a number of adv. phrs., used to mean to any degree whatsoever, which differ from the occas. adj. uses which are positive inversions of the usual not worth a...; see also under not worth a...

In phrases

worth a cent (also worth a busted nickel, ...a copper, ...three cents, ...twopence)

[mid-19C+] (Aus./US) a general negative intensifer, at all, to the least degree, e.g. you ain’t helping your Mom worth a cent (cf. not worth a cent phr.).