How to setup multiple way of authentication in Jenkins such as LDAP and Jenkins User database?

authentication jenkins

This is not possible as described. The feature request is JENKINS-15063.

However, it is possible to approximate in a few ways (though the Jenkins user database still won't be usable).

For multiple LDAP realms you can set up a single proxy server that combines the forests.
Using PAM you can define multiple authentication sources and fallbacks in e.g. /etc/pam.d/jenkins

authentication jenkins

Yes that's possible and requires 2 steps:

Add a user
Navigate to Jenkins -> Manage Jenkins -> Configure Global Security.
Under Authorization you need to configure who can do what. You can add LDAP groups and/or users and fine tune what they are allowed to do.
If you enabled Matrix-based or Project/Matrix-based authorization then you have a field to add new users/groups. You can add users that are known to LDAP or not known.
Add Credentials
If you added a user that is not known to LDAP you need to create the credentials in Jenkins (i.e. password).
Navigate to Jenkins -> Credentials -> System -> Global Credentials -> Add Credentials
Then add username and password.

CodeHunter