How to build a PHP remote application update system with Authentication?

Hey there! I have built an application in PHP. It is a paid application and contains a licensing system too.

Now, I want to provide automatic updates to my clients. How should I do it?

One important thing is the update URL should not be accessible by the normal public, only my registered application users can download the file.

To be simple, I want authentication to be done while downloading the updates too so that others can't get updates without buying my application.