My authentication calls an API of the other server, I don't have a database table(The username and password does not exist on my server).How do I use JWT authentication in this case? Thanks.
When You try to implement your own authentication server, you have to have a database with the username and passwords.
But after the user has its JWT Token, it can authenticate itself with it to your API Server, as long as the expiration time has not passed and the signature secret is shared between your auth and API Server, since you need to check if an attacker might have modified it.
After the expiration time has passed your client needs to issue a new token. You would usually use a second refreshToken which has a longer expiration time, and is checked against a DB to issue a new accessToken.
You could implement this yourself, but I would highly advise you to use technologies like OAuth2 since OAuth is used across all major brands like Google, Twitter, Github etc and is well tested against vulnerabilities.