If you're asking for an ability to show notifications directly on the screen when the phone is asleep, you would have been better off getting a Moto X, since that is a native function of its interface. If you try to do that on other phones, you'd probably have very high battery drain, as the phone would be keeping the screen on for much longer than it's designed.
That being said, you could try
DynamicNotifications, which lights up your screen when certain notifications come in. You could also try an app like
Easy Reminder, which can be set to give you repeated alerts for missed notifications.
