Hi, and welcome to Using English.
Usually (usually, not always!), a simple statement about not having something uses a plural. That's the general rule.
I don't have any bananas to sell you. (Yes, we have no bananas... if you're really an old student, you can sing along.)
I don't see any pens in the drawer where you told me to look. .
She doesn't have any brothers or sisters.
However, the phrase "I don't have a clue!" takes the singular - it's an idiom. You don't have any clue, do you? He just doesn't have a clue.
So the child not having any clue, versus any clues, works.
Student or Learner