FCM documentations states that

With FCM, you can send two types of messages to clients:

• Notification messages, sometimes thought of as “display messages.” These are handled by the FCM SDK automatically.

• Data messages, which are handled by the client app.

In your case, it seems that you are looking for Notification messages. In short, FCM will automatically display a standard android notification with a title and a message (body), when your app is in background.

To get this to work, the notification needs to be sent through Firebase (for example using the firebase console or cloud functions) and it needs to contain the notification key like in the following sample:

{
  "message":{
    "token":"bk3RNwTe3H0:CI2k_HHwgIpoDKCIZvvDMExUdFQ3P1...",
    "notification":{
      "title":"Portugal vs. Denmark",
      "body":"great match!"
    }
  }
}

For what regards your app’s side, it mainly just needs to be setup as a Firebase client. If in any case you want to receive/display the notification also when your app is in foreground, then you’ll have to create a service that extends FirebaseMessagingService as explained here

Bonus: since it looks like your target is android 8+, you may also want to look at Notification channels as every notification must be assigned to a channel in order to be displayed. By default, you’ll get one with basic settings.

Due to numerous app restrictions by android including Doze Mode and different OEM having their own implementation of battery optimization.

So I found out that GCM services is always running, is there a way for FCM to handle notification in background on its own?? Without depending on my app or app state?

I only send notification message which I want the FCM to handle without my app, because my app might be forced stopped or killed by app killers.

Can FCM just handle notification without my app’s involvement?