A smidgin is a tiny amount of something — much less than a normal serving. You use it for things you add a little of: 'a smidgin of salt', 'a smidgin of milk in my tea', 'a smidgin of butter'. It also works for things you cannot hold: 'a smidgin of hope', 'not a smidgin of proof'. It is a warm, friendly, everyday word, the kind of thing you say in a kitchen or in relaxed talk, not the kind of thing you write in a report. It often carries a small feeling of care — you are not just saying 'a little', you are saying 'only the smallest bit, please'. It very often appears in the negative to mean 'none at all': 'He hasn't got a smidgin of sense.' You will also see it spelled smidgen and smidge; smidge is the shortest and the most casual, and is what younger speakers say most. All three are the same word.