Question

On-site-notification works rather slow, is there any way to make it faster?

Answer 1

It is as "fast" as your server.

It just sends one ajax request if you click on the notification bubble. The respond time is up to your server, not to the plugin.

Answer 2

You're unlikely to get any helpful replies with such a vague question... you need to elaborate what part of notifications is slow, some info regarding your hardware, content volumes, no of users, volumes of posts etc