Here's the deal ... over the past month, there've been hundreds of sightings of drones in the Jersey sky -- with some said to be as big as a car -- and it seems no one knows where they are coming from or their purpose.

TMZ contacted several gun stores around the state ... we hear some people are getting strapped 'cause they are unnerved by the drones.

The Arsenal Gun Shop is one location where sales have spiked ... and, the owner tells us there has been a run on AR-15s due to drone worry -- with customers specifically saying they are buying for that reason.

Numerous other store owners told us that sales could not be definitively linked to the drones ... but the mystery certainly has been a topic of conversation inside the shops and spurred plenty of jokes.

As we previously reported ... if feds don't show definitive proof the drones are harmless -- or spring into action soon -- local politicians fear it's just a matter of time before citizens start shooting them down.

President-Elect Trump posted a message on his Truth Social platform Friday ... and, in true Trump fashion, he didn't mince words writing -- "Mystery Drone sightings all over the Country. Can this really be happening without our government’s knowledge. I don’t think so! Let the public know, and now. Otherwise, shoot them down!!!"

We spoke with Assemblywoman Dawn Fantasia ... and, she tells us there has been basically no information about the unnerving situation provided by the federal government or state leaders ... and, there's even confusion on which agency is actually running the show.

Mayor Tony Perry had similar gripes with the government ... and, both politicians are concerned people are going to start taking matters into their own trigger fingers.