"tiny amount," short form of smidgen, 1902, American English dialect.
Entries linking to smidge
smidgen n.
"small piece or quantity," 1845, perhaps from Scottish smitch "very small amount; small insignificant person" (1822). Compare Northumbrian dialectal smiddum "small particle of lead ore" (1821); ultimately a variant of smeddum "fine flour; fine powder," which is from Old English but of unknown origin.