Seat of the Cats
The fortress used to be the seat of the witcher School of the Cat, one of the splinter factions of the order established by Alzur. It served the monster hunters until around the end of the 12th century, when the royal army sieged the citadels and over the course of 3 days killed off all the witchers inside.
Some time after the castle was abandoned, mage Vilgefortz chose it as his hideout and a major base of operations. He created a magical whirlwind portal transporting ships from the Sedna Abyss to the place just outside the castle.
It was the location of the notable battle that took place when Geralt's company assaulted it in an attempt to rescue Yennefer and Ciri and during which many died on both sides, including Vilgefortz, Leo Bonhart, and all of Geralt's allies (Regis, Cahir, Milva, and Angoulême). Despite this, Geralt was successful and reunited with Yennefer and Ciri.
The Lodge of Sorceresses, who'd been trying to beat Geralt to Ciri to use for their own agenda, had originally thought they got the upper hand and attacked Rhys-Rhun Castle but quickly learned the witcher had outsmarted them and given them a false location. Shortly after Geralt's assault on Stygga Castle, the Lodge learned it'd been the real location and were too late in getting to Ciri themselves. As this wasn't in the Lodge's best interests, they dispatched Sabrina Glevissig, Keira Metz, and Triss Merigold to destroy the castle so the only legend surviving the events would be the false location, Rhys-Rhun Castle. The resulting explosion was heard as far as Maecht and the blast was seen as far as Metinna and Geso. Seismic shock also reached as far north as Oxenfurt Academy and destroyed the newly discovered perpetuum mobile.
This proved very effective, as nobody centuries later could find so much as a fragment of the castle and only one book about the legend, The Black Book of Ellander, mentions Stygga Castle as the location of the final battle.