How can I clone this behaviour (iOS) on an Android-App?
Technically its definitly possible as I have an app by my own on my Androidphone - its an Email-App with a very similiar indicator on the Icon. (shows the number of unread Emails)
If you are referring to doing this on the home screen, that is an app widget.
yes you can implement overlay like ios.. by the way it is called badge value.
here is one sample available on github
You just have to add classes in your project and call below lines
View target = findViewById(R.id.target_view);
BadgeView badge = new BadgeView(this, target);
badge.setText("1");
badge.show();
hope it helps.
来源：https://stackoverflow.com/questions/16083816/app-icon-create-an-overlayinformation-number