Green’s Dictionary of Slang

quay n.

also quee
[? quod n. (1)]

(US Und.) prison.

[UK]Scoundrel’s Dict. 18: Any Prison – Quee.
[US]Sun (N.Y.) 20 June 2/2: Off.—Don’t you remember me in ‘quay’ up there? Con.—Oh, were you there? I don’t recollect you—how long were you there? Off.—Six ‘spots.’ Con.—Was you indeed! I was there seven!
[US]A.G. Field Watch Yourself Go By 393: The boss [...] swore he would not allow a cheap poker player to do him. ‘Fix the olly! I gave him broads to the show! He’s right as a guinea! Fix him! Have this cheap Greene County bilk pinched. I’ll land him in the quay.’ All of this, interpreted, meant that the boss wanted the winner of the capital prize arrested and thrown into jail.

In compounds

grand quay (n.)

(US Und.) a state prison.

[US]Ladies’ Repository (NY) Oct. 316/1: Grand Quay, Penitentiary.
[US]Nat. Police Gaz. (NY) 26 Oct. n.p.: Gentle Annie [...] is sure to go to ‘grand quay’ as the thing can’t be ‘squared’.
[US]‘One Who Has Been There’ [J.H. Banka] Illus. History & Description of State Prison Life 492: Vocabulary of Slang Terms [...] State Prison...Grand Quay.
T.N. Doutney His Life-struggle, Fall, & Reformation 165: ‘I can have a chance to turn round and provide for her when she comes out of the grand quay’ (State prison).
[US]C.H. Darling Jargon Book 15: Grand Quay – State prison.