Idk if anyone had a similar problem before, but I live in EU by the countryside, at first there were only a few but now it happens more and more often to see drones passing over my house, I am sure they are civilian drones because law enforcement has no reason to use them since the area is quiet (and honestly I doubt they would be able to do so), however it bothers me enough to know that there are people who get over the fence and enter my property going to look at what they want, does anyone have any advice on what to do?
OP is in EU, but here in the US property owners do not have rights to airspace.
However, spying with cameras or nuisance noise would be reasons for legal action.
Could I shoot one down if it were spying on me?
Not in the US. You can report it to the police and the FAA, but it’s a federal felony offense to shoot down any aircraft, regardless of whether it’s a $100 drone or multi-million dollar full on airplane. But like the other poster said, voyeurism and harassment laws still apply. And also, if the pilot is out of sight of the drone, that’s a hefty FAA violation (assuming they don’t have a specific FAA waiver that’s hard to get) and something you can report.
In the US, you own the airspace up to the highest point of your property, including structures (and maybe trees). You also technically own your underground property to the center of the earth, but you may not have mineral rights to it.