how to send notification to specific user

firstly a great thank you for your great plugin
my question is:
how can we send push notification to specific user like categories wise subscription
i want to implement a function in which when user allow notification then category tag send to server to be store as user tag. and when we publish or update post than plugin filter and short user as tag with get_the_category() function and send notification to matched users

like that add javascript in pages to send category as tag to server to store with user information
and add a function.php code to short users with similler tag and send notification to them.