I live in the North Georgia Mountains. The neighboring remote control airfield was put in front of my house where my mountain view is. I have no issue with them flying over their lease, just not over my property and in front of my view. I have approached them to stop, but they refuse.
Do they have the right or can I have them served for trespassing?
I'm surprised that all the answers and comments so far have been about resorting to laws, other higher authorities, or anti-aircraft batteries, and that nobody has suggested being nice.
When you say that you approached them to stop and they refused, that sounds like you went and talked to people flying their RC planes. Presumably the RC airfield is leased by a club, which is probably legally organized as a non-profit corporation, which therefore has a board that meets regularly according to bylaws. In ordinary times I would suggest finding out when the club board meets, and paying them a visit. (With the pandemic stalking the land you're probably better off telephoning the club president or other club officer.) If you appear at the board meeting and identify yourself politely and state reasonable concerns without accusing anyone personally, then I would think most club boards would take your concerns seriously, raise the issue with the rank-and-file club members at the next regular meeting, put a strongly-worded notice in the club newsletter, and give you telephone numbers of several board members to call in case you have any more trouble.
Most clubs devoted to any hobby just want to pursue their hobby in peace, and in order to be left alone they need to be good neighbors, and so that's what most clubs try to do. It shouldn't be hard to get people to not fly over your property and close gates after they retrieve planes that accidentally came down on your land.
Then there is your demand that they not fly planes in your view. Are planes over their field in your view? In that case your demand may be neither legal nor reasonable. (Please know that I'm no lawyer.) Even so they may be willing to negotiate if asked nicely, and for instance offer to fly only three hours a day for two days a week just to avoid trouble.
The USA's national organization of aeromodelers advises pilots on page 4 of its safety guide:
It’s important that you respect the privacy and property of others and be aware of your surroundings. What might seem like a cool flight path to you may be a nuisance or perceived as invasion of privacy by others.
If they're an organized club (likely, as they're leasing their field), then ask them to follow these AMA guidelines; if they don't, complain to the AMA.
If they're not an organized club, complain to the AMA anyways. The AMA wants all radio-control pilots to behave courteously.
I think attacking this from an aviation regulation standpoint would be very difficult. The aviation authorities are hesitant to start naming specific property rights for air over property as the sky is public domain and the height of structures on property can vary significantly.
If they have cameras on those drones and they are recording, you might have better luck with pushing back on them recording without consent in a place that isn't open to the pubic where you have a reasonable expectation of privacy.
You've asked verbally and they've ignored you, so you should hire a lawyer and see how they can help you. Perhaps a formal cease and desist letter might make them be more courteous about your right to privacy on your private property.
Also, those drones need to be operated in a line-of-sight from the operator, so if you think there is no way the person at the RC airfield can see the drone with their own eyes from that field, then I would take video or photos of that position so you can demonstrate that they are violating the line-of-sight regulation and pass that along to a legal professional for assistance.
I would start with your township to see if there are any bylaws in that regard, then check with the county, then check with the State.
Barring that, your best bet would be to approach the owner of the property they are renting from and threaten to sue over loss of enjoyment, or have your lawyer send the owner a letter to that effect. If the RC group has some sort of organized or incorporated entity, you also might go after that.
