Android One Note Badge Function

You mean something like On the Facebook messenger appchethad.

http://www.piwai.info/chatheads-basics/ Here's an example of how to implement it.

<uses-permission android:name="android.permission.SYSTEM_ALERT_WINDOW"/>

You can display the view in Window by inserting the corresponding permission. And you have to keep floating, so you have to float it as a service, not an activity.