So I did some digging about Android Notifications and Building Notifications. You can set the icon by using the icon parameter.
However, for the Badge inside the notification, this one seems to be handled by the Android System itself and cannot be modified. Depending also on the device, it may very well be that the badge is not visible, since Android itself doesn't allow Notification Badges even for App Icons.
So far, I've done some testing on my device and only the notifications that show badges are the ones that can be opened by Google Apps (Gmail, Drive, Photos, etc.) and the notifications sent by Device Manufacturer.
The one you've included in your post must be a default badge made by the device manufacturer and it is only showing because of the Device's App Launcher.
So long story short, it's not possible for you to set the Notification's Icon Badge.