I just want to know if it's correct to use "if I may happen" on this example: "If I may happen to have what you're looking for..." English is not my first language so I'm confused about it.
If I happen to have what you're looking for...
is perfectly natural and implies there is a possibility that the speaker has the thing in question. It is certainly possible.
If I may happen to have what you're looking for...
sounds really weird but is technically correct, and implies the possibility that there is a possibility. Which is to say, it may be possible that the speaker has the thing. No idea when you would need this, however.
In conclusion, both are correct but I'm 99% sure you need to use the former (without may).
Hope this helps!