Here is the solution to your need, if you are running a Blogspot blog, you can also easily install blog notification service for free, though there are some limitations for free users. Here is what you need to do to activate notifications for your site in blogger. There is no option in blogger to do that, We will be using a third party service called push crew to install push notifications service on Chrome, Firefox, and Safari. Check Out Our Tutorial For Adding Push Notifications In Blogger .
1. Register your free account here: PushCrew
2. Click on Signup for Free and Enter your registration details and the URL address of the blog you need to install push alerts.
3. Now Login to your dashboard. Click on Settings > Get Code
5. Click On Customise for Desktop. Now, You can customise the color of the alert window, upload your blog logo or even modify the push notification text message.
6. Once completed, Click On Save! Done, Now your Site Users Will receive a notification on their browser for the first time they visit your blog. Once they click on allow, they will be subscribed to receive every alert which you create and send from your dashboard.
So, Every time you create a new post, you can send them notifications to bring them to your site, even if they are not browsing your site.
As, you are using the Free Version of PushCrew, You will not be able to activate the push notifications for Mobile Devices, and also subscriber limit is 500. Once you reach the limit, you need to upgrade for more subscribers.