Yes, apparently it's a thing.
Americans seem to make sport of almost anything, and today’s example is no exception. Several sportsmen made lemonade out of lemons when it came to the invasive species of fish dubbed Flying Carp that’s been plaguing southern boaters since the 1970s, and have reached as far north as Minnesota. Silver Carp, or Asian Carp, are termed Flying Carp because they literally fly out of the water when startled by a boat motor. The carp in question have caused injuries to boaters and have raised concerns over the aquatic ecosystems they’ve invaded. People have taken to catching them with nets in the air, hitting them with baseball bats, and shooting them with bow and arrows… and most recently, shooting them with shotguns.
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The Clarion-Ledger reported that two Mississippi residents have been having loads of fun blasting the Flying Carp as they come out of the water. On one outing, they went through more than 500 rounds. They clarified that they were only shooting on a privately owned lakes and that it’s not legal to conduct their newfound sport on the Mississippi River.
One of the men explained that they stick to 20 gauge shotguns for the reduced recoil and due to the high volume of shooting. They did say that if anyone else wants to try shooting Flying Carp, they should be proficient with firearms first, as you don’t want to put a hole in your boat or motor.
There's more at the link.
It seems this isn't a new idea. A quick search turned up this video clip from 2014.
There are also plenty of videos of bow-hunting flying carp with arrows. Since it's an invasive species that needs to be kept in check, such methods are apparently fine with nature conservation authorities.
However, I still think I had the best idea for hunting aquatic life with shotguns, while on vacation at the Gulf Coast some years ago.