Hi Juan,
Thank you so much for the response, after installed the local_mobile plugin, the push notification works on moodle's original app with moodle 3.1.
However, I have created the customize moodle app, set up the own airnotifier server and configured all server/app settings on moodle site, like Airnotfier url, port, app name etc.
And, I also enabled the message notification from "user profile" and "Manage message outputs" page.
But with this customized app the push notification is not working. When I see the message preference from user profile it shows below message.

When I do print_r($resp); at create_token function in message/output/airnotifier/classes/manager.php, which shows
{"status": "token exists"}
Why push notification is not working ? Can you please give some guidance on this?
Thank you for your effort.