Supe Kitchen. The Ninth Circle. PowerMax. Countless other monickers that one can ascribe, though there is one that is almost universally recognisable.
The Borehole
Somewhere in the Rockies
ADX Florence was something of an inspiration for it, as far as security and retention was concerned. Except in this case, it was for those who weren't just defined by their humanity - that were greater than their mundane counterparts. An element-bender here, a nigh-unstoppable, mutating behemoth there. Prisoners that held a status far above their mundane counterparts.
Any world with its so-called supers, metahumans, abnormals, demigods, whatever you'd call them - would find a need for a place like this. Miles apart from civilisation, behind literal ironclad perimeter defences and buried under what feels like a mile of rock There are, of course, other places like this - but the Borehole stands out as the example - the standard by which prisons of its caliber are measured. To date, none have got in or out without the system's say-so.
You, or specifically, your character is an inmate here. Perhaps a recent transfer. Perhaps not so much. Whoever you were. Whatever you did, whatever or whoever you damaged, modern society judged you unfit to remain walking free among its denizens - so they sent you here.
Countermeasures specific to your circumstances have been in place from the moment you walked in. Maybe there's an electrified ankle bracelet to prevent you from phasing out of your cell. Maybe you're kept in constant light to avoid drawing sustenance from the shadows. Or perhaps you're just given a dairy-free diet, so you don't try and wrap cords of cheese around some other poor bastard's brain stem like that obnoxious regenerator working for the white hats.
Either way, an opportunity is about to rear its ugly head. Freedom might be yours.