Displaying a fullscreen notification

We are building an app that uses WebRTC (and maybe SIP). We would like to show the user a ‘fullscreen notification’ when our application user receives a call, even when the application does not run in the foreground.
Anyone have an idea howto start?

Think like a Skype, SIP or whatever calling app. You sing into those apps and after sigining in when you receive a call you have a ‘fullscreen notification’ when someone is calling you even when you are not actively in that app.

When I search the net I can’t find anything related to this. Maybe we need to build some native code? But if we do, how do we release this native code together with the Cordova/Ionic app?