I am developing a web app using Laravel, But I have to integrate the mobile application in the future. Now I want to ass API Authentication passport. I am a little bit confused how passport API handle multi auth system form multiple user and permission systems. Currently, I am using Laravel default auth to handle user. Is there any library for Laravel multi auth using API Authentication passport??
The thing you have to understand about Passport is that it is nothing more than a Laravel wrapper of the oAuth2 framework, specifically this implementation: https://github.com/thephpleague/oauth2-server
As such, you must understand how the different oAuth2 grant types work. I recommend reading up on oAuth2 to familiarize yourself with the concepts (I personally found this site to be the most helpful for understanding the different grant types: http://www.bubblecode.net/en/2016/01/22/understanding-oauth2/).
Specifically to your question, take a look at Password Grant Tokens (https://laravel.com/docs/5.6/passport#password-grant-tokens) for use in a mobile app. Once you have your token, Laravel handles all the Authentication behind the scenes and you can use Auth::user() as you would normally, assuming you have Passport set up and configured correctly; the user is tied to the token and is independent of any other token and any logged in user.
As for permission systems, Passport uses scopes (https://laravel.com/docs/5.6/passport#token-scopes) which is a handy way of limiting what routes your tokens have access to. Aside from that, permission management for the Auth::user() is the same as any other user using your application.
EDIT:
Passport scopes are used to lock down routes, so they can be used. However, Passport is only concerned with authentication (ie, is this user valid) and NOT with authorization (ie, what can this user do). How you authorize users to do different things is 100% independent of Passport and is up to your web app.