This is not a "notification", this is an element on the page that asks you to enable notification.

The website simply does not check whether you denied notifications, it just checks whether you enabled them, or clicked on "Not now".

But my settings are not to show/ask for notifications.

Yes, Chrome will not ask you, it will deny their request immediately. But Chrome does not control the way the website decides to ask you as well.

Unless new information arrive, I think this is a website user experience issue and not a browser issue. Closing.

I am curious - you indicated that this "works" on other browsers - on which browser does it work?
(Note that Safari, Internet Explorer and Edge do not support push notifications at all at the moment, so the website intelligently does not ask on those browsers, it only asks on Chrome and Firefox. Unintelligently, though, it will only ask on Chrome and Firefox and maybe Edge, even if other browsers support this.)

Yes it is supported in chrome and firefox only but i hope api will be updated in such way that it will match user defined settings.

Again, there is an API that provides the needed information to tell the website that the user has blocked notifications. This specific website simply does not try to detect it, it only tries to detect whether the user answered their request to show notification.

If they try to use the Notification.requestPermission() API (which would normally cause the browser, not the website, to show a permission request bubbue from the address bar), it will immediately get a rejection (and no bubble will be shown).

To summarize, you should contact the website and ask them to fix its implementation to stop harassing you. :(

*bubbue = bubble

For future reference, the API to detect the current permission status is Notification.permission.

Makes sense. I totally agree with you, but doubt they will update this.