Question

He persists _____ teasing the other children in the class.

Answer 1

if it is preposition then it's answer is on

Answer 2

The most appropriate answer to the question is ‘in’.

The complete sentence will be as follows:

He persists in teasing the other children in the class.

Given below is a sentence extracted from the Cambridge Dictionary that will make the things more clear.  

“If he persists in asking the awkward question, then send him to the boss.”