I have created an App with Apple Watch extension.
I would like to know if it's possible to schedule a notification that only appears on the Apple Watch. And conversely, can we schedule a notification to only appear on the iPhone?
This is a great question, but unfortunately it is not possible at this time. Apple is trying to be very pragmatic about how they direct notifications. If you iPhone is unlocked, they assume you are looking at it and will route notifications there. If you iPhone is locked, then all notifications will be routed to your Apple Watch. They want to avoid duplicated notifications in both locations at all costs.
Currently there is no ability to force route remote or local notifications directly to the Watch only. If you feel strongly about this feature, then I would suggest you file an enhancement radar with the Apple Bug Reporting System.