Use WP login cookie for my PHP site

Hello I think this is the right forum
I would like to integrate my WP login system with my other PHP project.
My WP is installed om example.com and my other project is on a sub-domain eg. sub1.example.com.
I found this code:

require('../web/wp-blog-header.php');

if ( is_user_logged_in() ) {
echo 'Welcome, registered user!'.$user_email;
} else {
echo 'no';
};

This works and gives me the mail of the logged in user. I put the script on the main domain example.com/wp.php

But my PHP project is on the sub-domain and if i move the script to the sub-domain it stops working. If I access the PHP site and every page where I include the ../web/wp-blog-header.php file it will redirect me to my main site at example.com. ??
I also tried to fix this and added:

define('COOKIEPATH', '/');
define('COOKIE_DOMAIN', '.example.com');

ut this din’t do any thing.

How can I get the relult I want? or is there any plugin or other method?
plz help!