Until now I used development push certificate and the push notifications worked great.
Now I want to submit my app to Apple so I created a production certificate a
The production push will work when you download the app from the App Store.
UPDATE:
You can also test the production push with an AdHoc build of the app; see Trinca's answer.
UPDATE:
Now, the easiest solution is to use Apple's TestFlight. (In TestFlight, it is easy to add new remote users, sending them an email invitation, they then download on whatever device they choose.)