is there any the address lookup api globally

Do you mean lookup of personal street addresses? Not that I know of, unless you count Google 🙂

Yes personal address like I start typing and it start showing addresses matching

From what set of people? Anyone in the world? How do you choose from duplicate names? Or are you really not asking about address lookup, more about typeahead lookup from your own data?

the post office maintains a service, but only for US addresses. I doubt there's anything with complete address verification for the whole planet.

I found one Positionstack.com

That looks like geocoding, not lookup of people's addresses. If that's what you need it looks cool, free even unless you do a lot.

I have to try to see if it can provide address So if I go with google It’s gonna be pricey right

Bing also has a lookup service for mapping if that's what you're looking for...

Do you have its actual url where I can see