Green’s Dictionary of Slang

not worth a tinker’s damn phr.

worthless, useless.

1863		Goulburn Herald (NSW) 11 Mar. 4/1: You will see a subscriber take up his news paper [...] and, after perusing it for an hour, throw it down in disgust, affirming (in bush slang) [...] that it is not worth ‘a tinker’s curse’.
1903		J. Furphy Such is Life 144: ‘Hides like that o’ yours [...] ain’t worth a tinker’s dam for standin’ the sun.’ (For the information of people whose education may unhappily have been neglected, it will be right to mention that the little morsel of chewed bread which a tin-smith of the old school places on his seam to check the inconvenient flow of the solder, is technically and appropriately termed a ‘tinker’s dam’).
1909		L.W. Payne Jr ‘Word-List From East Alabama’ in DN III:v 382: tinker’s dam(n), n. phr. A worthless thing.
1913		Libby Herald (MT) 8 Aug. 1/2: He says the land is rotten, / Not worth a tinker’s d—n.
1914		G.A. England ‘Rural Locutions of Maine and Northern New Hampshire’ in DN IV:ii 83: wuth a tinker’s durn, not, adj. phr. Good for nothing.
1935		J. Conroy World to Win 272: I brought back [...] a head full of fool notions, but not a page of writing worth a tinker’s damn.
1941		P.C. Wren Uniform of Glory 45: Notr being worth a tinker’s damn, and of less use and value than the butt end of a dead bed-bug.
1943		‘Myles na gCopaleen’ Faustus Kelly in ‘Flann O’Brien’ Stories & Plays (1973) 179: T’isn’t worth a fiddler’s curse.