I deal with this all the time locally on a few social media Next door neighbor web sites... Concerned about spying citizen wants to know best way to shoot down a drone
The problem many do not understand is there are a LOT of very legitimate drone operators doing a lot of Legal and lawful surveillance from the air and a home owner can NOT distinguish those drones from the Peeping Tom Neighbors drone or the neighborhood kids wall-mart toy
So Yes YOU do have a right to protect your property..BUT only from the Peeping Tom.... BUT shooting down a LEGITIMATE drone is a FELONY
Sheriff looking for lost child
Animal control surveying Hog concentrations
County Land use survey
Real estate aerial photo of adjacent property
State Game warden doing surveys
Local water provider doing surveys
and on and on
These all are licensed contractors ...and for the most part, with some very expensive equipment: WITH GPS and very good cameras.... the Exact position of the craft is recorded, and the good video of you aiming and shooting is recorded.
I can say with some certainty IF you deliberately shoot down a Legitimate drone it is going to be investigated and at the least you will be liable for the loss of property and the owner has a good set of facts to send the Sheriff
Then there may also be the discharge of firearm in a forbidden place ( city/town) to deal with
As to who owns the air space directly above your property...well it is a depends situation...There is settled case law that now claims Legitimate licensed entities may overfly "at any height" personal property...used to be 400 foot.
The two drone operators I know absolutely still use the 400 foot just to keep their operations out of that quagmire but there are situations where a closer look is needed ( looks like child body at base of a tree)
So a drone is hovering 50 foot over your back yard and looking under the tree canopy over your fence to find something, or some one, and you shot it down...Police or sheriff is gonna come knocking and your claim it was peeping is not gonna hold much legal water
Point is there are a lot of these doing legitimate and good work and there will be more in the future... even commercial ventures by Amazon/Walmart/Wholefoods/Dominoes etc to deliver to you or a neighbor
So while the knee jerk to shoot sounds manly and righteous...just not worth the grief IMO