Green’s Dictionary of Slang

smidge n.

a very small amount.

1905		L. Pound ‘Dialect Speech in Nebraska’ in DN III:i 65: smidge, smitch, n. Smallest piece, tiniest particle. ‘They ate every smidge of fudge.’.
1934		Sun (Baltimore) 21 Sept. 1/6: Every last smidge of his record will be investigated [OED].
1945		Oakland Trib. (CA) 13 June 7/2: ‘Not even a teeny wenny smitch?’ asked jangle. ‘Not even a smitchy, witchy tee!‘.
1967		‘Ellery Queen’ Face to Face 184: Do you suppose I might have a smidge of that, Inspector? It looks so good, and I haven’t had any breakfast. Or dinner last night .
1973		Observer 28 Oct. 48/4: Inviting us to buy their mail-order course for a smidge under £13 .
1997		L. Davies Candy 205: Have you got anything, mate? Just a smidge?
2000		I. Rankin Set in Darkness 246: Well, maybe just a smidge.
2007		S. Maloney Sucked In 60: I was feeling peckish. Time for a smidge of the fast and easy.

In phrases

tip the smidge (v.)

to short-change.

1825

‘Shadrack the Orangeman’ in Universal Songster I 27/2: Tinks vat he has done the Frenchman, tip’d him de smitch, and all dat.