How to send browser push Notification using asp.net web-forms?

You should use javascript plugin provided by Mozilla Developers Network

https://developer.mozilla.org/en-US/docs/Web/API/notification

If you want to trigger notifications from the server side, rather than from the client side, then take a look at SignalR:
http://signalr.net/

There is a plugin also available here https://alxgbsn.co.uk/2013/02/20/notify-js-a-handy-wrapper-for-the-web-notifications-api/

Its working sample here https://alexgibson.github.io/notify.js/

There is another way to add push notification in your website without using much of the code,that is using https://subscribers.com/ you just need to add some javascript on your website or add code in your GTM and that's it you are done.

Subscribers allows you to create "Welcome Drip" also, with the help of which if user subscribe to your website, you can send user some notifications as Welcome messages.

You can create notifications using Javascript, here is sample JS code

(async () => {
    // create and show the notification
    const showNotification = () => {
        // create a new notification
        const notification = new Notification('JavaScript Notification Example', {
            body: 'This is a JavaScript Notification API demo',
            icon: './img/js.png'
        });

        // close the notification after 10 seconds
        setTimeout(() => {
            notification.close();
        }, 10 * 1000);

        // navigate to a URL when clicked
        notification.addEventListener('click', () => {

            window.open('https://qawithexperts.com/questions/173/how-to-send-browser-push-notification-using-aspnet-web-forms', '_blank');
        });
    }

    // show an error message
    const showError = () => {
        const error = document.querySelector('.error');
        error.style.display = 'block';
        error.textContent = 'You blocked the notifications';
    }

    // check notification permission
    let granted = false;

    if (Notification.permission === 'granted') {
        granted = true;
    } else if (Notification.permission !== 'denied') {
        let permission = await Notification.requestPermission();
        granted = permission === 'granted' ? true : false;
    }

    // show notification or error
    granted ? showNotification() : showError();

})();

OR

You can also use various push notifications API which can be configured using Javascript and easy to use.

1. https://onesignal.com/

2. https://pusher.com/beams

3. https://pushy.me/docs/api/send-notifications (You can send notifications using .NET in this)

4. https://www.webpushr.com/