Green’s Dictionary of Slang

(US campus) shut up! an expression of disdain.

1908		Rock Is. Argus (IL) 20 Feb. 6/4: ‘Here, you foreigners,’ said he, ’quit it! Let up, I say!’.
1957		W.R. Burnett Underdog 86: ‘I feel so sorry for that poor girl.’ ‘Oh, quit it, Rhea,’ said Dan. ‘You’ll be trying to get him to marry her next’.
1986		Eble Campus Sl. Mar. 8: quit it – expression of disbelief: ‘Too much sun causes wrinkles.’ ‘Oh, quit it!’.