The most common and most likely answer to this crossword clue is the 3 letter word WHY
I've seen this crossword clue in The Daily Telegraph
W
H
Y
More clues leading to the result WHY
Buddy explains!

The straight part
We know that "Question of puzzlement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case question of puzzlement = why.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does WHY mean?
WHY noun- Reason
- For what cause, reason, or purpose (interrogative adverb).
- For which cause, reason, or purpose (relative adverb).
- An exclamation used to express indignation, mild surprise, or impatience.
- A young heifer.