More than one etymological thread might be involved here. The word itself seems to have confused literary English from the beginning. The word quiz, as in "to question," can be traced back to 1847 spelled as "quies", meaning "to examine a student orally." It is likely derived from the Latin expression qui es? "who are you?," the first question in oral exams in Latin in old-time grammar schools. The modern spelling quiz is recorded by 1886, though it was in use as a noun spelling from 1854, perhaps in this case from the slang word quiz "odd person" (1782, source of quizzical); an earlier verb from that sense was quizify "turn (someone) into a quiz" (1834).

Source: Etymology Online