I am able to make this possible by creating two plugins in wordpress the first one is referencing a existing plugin ext_db_auth and the other one is using below code referencing here.

Hope this will be useful for those who are seeking for the same functionality.

add_action(\'init\', \'myStartSession\', 1);
add_action(\'wp_logout\', \'myEndSession\');
add_action(\'wp_login\', \'myEndSession\');
function myStartSession() {
if(!session_id()) {
session_start();
}
}
function myEndSession() {
session_destroy ();
}

You must import your user\'s table to WordPress users.

The best practice its to convert your site to WordPress theme.

But if it\'s heavy for you, you have more option as follow, In order of priorities in descending order:

1. Import users and change from now the login to wp-login.
2. Import users but use wp_signon function.
3. Use your regular site header and footer instead WordPress header & footer.