Looking for alternatives for email notification

Hello,

I have googled to find a plugin that can replace the original email notification when there is new comment.

For example: A (log-in user) writes a comment in a post, and then B writes another comment in that post. So A will receive an notification like this:

And when A clicks on the icon, it will show the notification in detail, like this:

Anyone who knows if there is anyplugin can do that job?

Thanks