Green’s Dictionary of Slang

a derog. term used for a young man.

1604		Shakespeare Othello V i: I have rubb’d this young quat almost to the sense, And he grows angry.
1609		Dekker Gul’s Horne-Booke 30: Whethyer he be a young Quat of the first yeeres reuennuw, or some austere and sullen-facd steward.
1623		Webster Devil’s Law-Case II i: O young quat, incontinence is plagu’d In all the creatures of the world [N].