Uncertain; OED (3rd edition 2007) says that the origin of the phrase is unknown and states that a common suggestion is that the phrase originates with the distinction of the minuscule letters p and q in either the school-room or the printing-office, but goes on to say that the chronology of the senses argues against this since no such connotation is evident in the earliest quotations.[1]
In the early 17th century, however, there is the expression pee and kew in the sense of “highest quality, best possible”.[2] Also recorded as in thy Pee and Kue in 1602.
Alternatively folk etymology claims that it comes from the sense that Ps and Qs mean 'Pints and Quarts' which were listed as 'Ps and Qs' before payment. The phrase would then come from minding your alcohol consumption as a result
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mind one's ps and qs (third-person singular simple present minds one's ps and qs, present participle minding one's ps and qs, simple past and past participle minded one's ps and qs)
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