In the North, the Witch-king’s fortress was Carn Dûm, the stronghold and capital of the realm of Angmar.
Angmar was founded in the Third Age by the Lord of the Nazgûl, who became known as the Witch-king of Angmar. From Carn Dûm, in the northern Misty Mountains, he directed his campaign against the divided Dúnedain successor kingdoms of Arnor: Rhudaur, Cardolan, and Arthedain.
The fortress is closely linked with the fall of the Northern Kingdom. The Witch-king eventually destroyed Arthedain and captured its capital, Fornost, but Angmar was later defeated by an alliance involving Gondor, the Elves, and survivors of Arnor. Carn Dûm itself was destroyed around Third Age 1975.
A common mix-up is Dol Guldur, another major fortress associated with Sauron’s forces. Dol Guldur stood in southern Mirkwood and was connected with Sauron, while Minas Morgul was the later stronghold of the Witch-king in Mordor’s orbit. Barad-dûr was Sauron’s tower in Mordor, not the Witch-king’s northern fortress.