The Notifier for GitHub extension allows you to check the unread count for any GitHub notifications you receive. You don't need to download any other add-on for it. Just install this and add your GitHub token in the options page.

Once you install the extension, you will see a small icon on the top right of your browser. Just tap on it, and you will see a new tab opened with your notifications page. You can find all the unread messages there. If there is any new notification, you will see it listed in the tab. If you have already opened the notifications page, it will not appear there.