misquote (v.)

1590s, "misconstrue, misinterpret;" see mis- (1) "badly, wrongly" + quote (v.). First recorded in Shakespeare.

Looke how we can, or sad or merrily, Interpretation will misquote our lookes. ["I Hen. IV," v.ii.13]

The more usual modern sense of "cite incorrectly" is by 1690s. Related: Misquoted; misquoting. As a noun, "an incorrect quotation," from 1855.