It might depend on why you're quoting but I think, in general, it would be better to quote the character, referencing the play with Act and Scene citations.

"[W]hat says Quinapalus? 'Better a witty fool, than a foolish wit.' " Clown, Twelfth Night Act 1 Scene 5.

In this case the character is himself quoting someone, although whom, is an unanswered question.