I believe you do technically own up to a certain altitude of airspace above your property, however any and all airspace is still under the jurisdiction of the FAA. The big one for the FAA is creating a scenario where something falls from the sky and could cause damage. That's why you can get in deep shit for even shooting at a personal drone with a BB gun, let alone birdshot.

I think you do, to a certain height. It’s probably like 100’ or less and probably varies by location

So if your location has such a law and the drone is over your property below that height maybe you have trespassing claim