Green’s Dictionary of Slang

an imaginary person, usu. used in a rude reply to an irritating question.

1835		G. Kent Modern Flash Dict. 9: Cheeks – an imaginary person; nobody; as, who does that belong to? Cheeks.
1848		Flash Dict. in Sinks of London Laid Open.
1849		Paul Pry 29 Jan. 4/1: Cheeks, the Marine, to accept his thanks; and the following me­ dical men strictly to attend to his admonition.