Green’s Dictionary of Slang

(US) 25 cents, a quarter.

1915		Wash. Post 28 Mar. n.p.: The word comes from the slang of the street arab, who has a name for every coin. A ‘meg’ is a cent, a ‘jit’ or ‘jitney’ is a nickel, a ‘dimmo’ is a dime, and a ‘cute’ is a quarter.
1917		Cincinnati Enquirer (OH) 12 May 12/2: ‘I made a souse for a cutey (25 cents) that night and flopped on it’.
1927		C. Samolar ‘Argot of the Vagabond’ in AS II:9 390: A quarter, a kyuter.
1929		V.W. Saul ‘Vocab. of Bums’ in AS IV:5 342: Kuter — A quarter dollar.
1931		Irwin Amer. Tramp and Und. Sl. 118: Kuter. – Twenty-five cents, merely a play on the word ‘quarter’ (of a dollar).
1933		Ersine Und. and Prison Sl. 60: quter, n. A twenty five-cent piece.
1946		J.E. Dadswell Hey, Sucker 87: A kuter is a quarter.
1950		Goldin et al. DAUL 54/2: Cutor. Twenty-five cents; a quarter.
1953		W.L. Alderson ‘Carnie Talk’ AS XXVIII:2 115: cuter, n. A quarter of a dollar.
1962		Ragen & Finston World’s Toughest Prison 807: kuter – A quarter (25$).