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1845, perhaps from Scottish smitch "very small amount; small insignificant person" (1822). Cf. Northumbrian dialectal smiddum "small particle of lead ore" (1821).
[1886+; origin unknown; possibly fr Scots Gaelic smidin, ''small syllable, hence tiny quantity''; found by 1845 as smitchin and by 1878 as smidgeon]