Green’s Dictionary of Slang

damn n.

also dam
[the orig. ety. is based on the dam, a low value Indian coin, but the widely assumed link is to the oath damn! excl.; the inclusion of ‘twopenny’ was apparently popularized by the Duke of Wellington (1769–1852)]

[late 18C+] a minuscule or virtually non-existent amount; often in not give a damn v.

In phrases

give a damn (v.)

see separate entry.

not give a damn (v.)

see separate entry.

not matter a damn (v.)

see separate entry.

not worth a damn

see separate entry.