Not really an expert in shotguns myself by any chance, but I believe that, while there wearen't shotgun-miniguns or shotgun-chainguns, I do think there are 'shotgun-like' autocannons, that actually just fire specialized ammunition.
For instance, the German [35mm Nächstbereichschutzsystem MANTIS Air Defence System](https://en.wikipedia.org/wiki/N%C3%A4chstbereichschutzsystem_MANTIS) uses shells named AHEAD ("Advanced Hit Efficiency And Destruction") that are basically very big shotgun shells: They have around 152 tungsten projectiles inside that, upon reaching an aircraft, explode, sending fragments in a conical area in front of the shell, damaging the aircraft
MANTIS ADS
![medium](https://www.bundeswehr.de/resource/image/4918240/landscape_ratio16x9/600/338/df98e032a8dfdf6d82e07bed6bf224d8/A4656A2FDAFEF2F6840D78EC5B142F93/mantis-rauch-schraeg-oben-hinten-en.jpg)
'AHEAD' shell
![medium](https://i0.wp.com/militaryleak.com/wp-content/uploads/2022/07/rheinmetall-awarded-e65-million-contract-to-supply-skyguard-3-air-defence-systems-2.jpg?ssl=1)
There are also other ammunition like that, such as the 20mm DM 111
![medium](https://www.men-defencetec.de/wp-content/uploads/Munition/231019.jpg)
And a MBT (M1A2 Abrams) has available shrapnel shells too
![medium](https://i.ytimg.com/vi/KJFEXdraEg0/maxresdefault.jpg)
(All images are medium sized by Derpibooru to not annoy users >.<'. You can open them on a new tab)
These are often called ['Shrapnel shell'](https://en.wikipedia.org/wiki/Shrapnel_shell), though IIRC there are also ['Canister shells'](https://en.wikipedia.org/wiki/Canister_shot) which might fit what you're looking for, in any case, while there are autocannons, big cannons, and artillery that can fire shrapnel shells, I kinda doubt of the utility of a minigun with shotgun-like shells... (Miniguns are 7.62mm caliber, and they're called miniguns because they're basically the smol version of the 20mm Vulcan. The stuff that look like miniguns but aren't actually miniguns in caliber are named rotary cannons), autocannons/chain guns and rotary cannons though... It's feasible, and they might be useful for anti-aircraft and anti-missile defence.