There are no English conjunctions that start with Q. The language has about fifty common conjunctions, from “and” and “but” to “although” and “whereas,” and none of them begin with this letter. Q is one of the rarest starting letters for any type of function word, which makes the gap easy to miss but hard to fill.
The reason is how English built its small set of connecting words. Most conjunctions come from Old English and Germanic roots, where words like “and,” “but,” “if,” and “while” developed. Words that start with “qu” mostly entered English later through French and Latin, and they tend to be nouns, adjectives, and adverbs, such as “question,” “quiet,” and “quickly.” Conjunctions are a closed class, which means the language almost never adds new ones. Once the list was set, there was no room for a Q word to join it.
A few words come close but do not qualify. “Quite” is an adverb that adds strength to another word, and “quoth” is an old verb meaning “said.” “Qua” is a Latin-based word that means “in the role of” and works as a preposition. Other languages do have conjunctions that start with Q, such as the Italian “quando” (when), but these are not English words. If you are looking for conjunctions in general, the lists for other letters, like B, S, and W, have many more options.