Login with WordPress.org site

I’m looking for a solution for using my wordpress site as the main user system to login with. Like WordPress has there “login with wordpress” I want my version of login with my wordpress.org installation.
I’m trying to build som kind of api.

I have tries including the wp-blog-header.php but it doesn’t work outside of the domain, and I have a few sites on there own domain.

Can I use wp-rest api to get current logged in user like wordpress.com dose? I downloaded wp-rest api as a plugin.

What more can I try?
I’m programming in PHP. The information I want to get from wordpress is something like id ,name, email.
// Victor