quigelj
No, there is no English word that starts with "q" and ends with "j."
There are no valid English word that starts with J and ends with Q. For reference, here are all the words that end with Q but none start with J: suq. tranq. umiaq. qepiq.
queenq kivi
quotes
quail
Quil
Quaint is a 6 letter word that begins with the letter q and ends with t.
quirky, quacky, quickly
queens
quitterquieter
quadquid
The word is "souq."