mid-14c., coitidian, "daily, occurring or returning daily," from Old French cotidiien (Modern French quotidien), from Latin cottidianus, quotidianus "daily," from Latin quotus "how many? which in order or number?" (from PIE root *kwo-, stem of relative and interrogative pronouns) + dies "day" (from PIE root *dyeu- "to shine").
The qu- spelling in English dates from 16c. Meaning "ordinary, commonplace, trivial" is from mid-15c. Quotidian fever "intermittent fever" is from late 14c. The noun meaning "something that returns or is expected every day" is from c. 1400, originally of fevers.