I am sending push notification to users which when clicking on it opens the app.
My problem is that when the app is already open, clicking on the notification start
Use a "launch Intent" for your app, like this:
PackageManager pm = getPackageManager();
Intent launchIntent = pm.getLaunchIntentForPackage("your.package.name");
PendingIntent contentIntent = PendingIntent.getActivity(this, 0, launchIntent, 0);
Replace "your.package.name" with the name of your package from the Android manifest.
Also, you should remove the special launchMode="singleTask" from your manifest. Standard Android behaviour will do what you want.