Wordorigins.org

The origin of the phrase mind your Ps and Qs, meaning to be careful of one’s behavior, is not known. Explanations for the phrase abound. Some are plausible, some are not. Let’s start with what we know.

The phrase dates to at least 1779 when it appears in Hannah Cowley’s Who’s The Dupe?:

You must mind your P’s and Q’s with him, I can tell you.