Solution:
For that above requirement, you need matching username/password with WP site.
When users are trying to register into your site use wp_create_user( $username, $password, $email );
and when users are logging into your site you can use following code
$creds = array(
'user_login' => 'example',
'user_password' => 'plaintextpw',
'remember' => true
);
$user = wp_signon( $creds, false );