Student or Learner
I have always believed that we say "on purpose" not "in purpose".
Do we ever say "in purpose"?
Not a teacher
No, it isn't correct. For instance, you could say either "he did it on purpose" or "he purposely did it".
You can use 'in purpose', but not as a substitute for 'on purpose'
These studies are commendable in purpose,
Jimmy Wales set out to build a massive online encyclopedia ambitious in purpose and unique in design
'The secret of success is constancy of purpose.' - Benjamin Disraeli. Here you could use 'in' instead of 'of'.
Your purpose is your aim or intention. As the object of a preposition it becomes part of an adverbial.