Three of the Nazgûl were mighty Lords of Númenóreans

The Silmarillion - Akallabêth said:

Yet Sauron was ever guileful, and it is said that among those whom he ensnared with the Nine Rings three were
great lords of Númenórean race.

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As the Whitch-king was the most powerful of the Nazgûl is is widely suspected that he was one of these Númenóreans. Those men who recieved one of the nine Rings became great kings, sorcerers and warriors:

The Silmarillion - Of the Rings of Power and the Third Age said:

Men proved easier to ensnare. Those who used the Nine Rings became mighty in their day, kings, sorcerers, and warriors of old. They obtained glory and great wealth, yet it turned to their undoing. They had, as it seemed, unending life, yet life became unendurable to them. They could walk, if they would, unseen by all eyes in this world beneath the sun, and they could see things in worlds invisible to mortal men; but too often they beheld only the phantoms and delusions of Sauron. And one by one, sooner or later, according to their native strength and to the good or evil of their wills in the beginning, they fell under the thraldom of the ring that they bore and under the domination of the One, which was Sauron's. And they became for ever invisible save to him that wore the Ruling Ring, and they entered into the realm of shadows. The Nazgûl were they, the Ringwraiths, the Enemy's most terrible servants; darkness went with them, and they cried with the voices of death.

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Btw this quote is twisted on Tolkien Gateway:

Tolkien Gateway - Witch-king said:

he gave nine of them to Mannish kings, sorcerers and other warriors.

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It seems here that the men were great kings, sorcerers and warriors before they got the rings. But the quote from Silmarillion (which they refer to) clearly says the opposite.
I also heard quite often the Witch-king was a "Black Númenórean" one of those who followed the King of Númenor to worship Melkor. But the Nazgûl appeared first in S.A. 2251 according to Appendix B of LotR about 1000 years before Sauron came to Númenor.

Now about sorcery. Most magic in Tolkiens writings is quite subtile. There are no magical fights like Gandalf and Saruman in the movie.
I made a list of all effects I can think of:

• Sauron's main power is to influence or control other beings like Elven smiths of Eregion and his orcs and trolls. Those start to fight each other when the ring is destroyed.
• Elvish mental communication e.g. Galadriel testing the members of the Fellowship in Caras Galadhon or Gandalf calling for Shadowfax over long distance.
• Thrór said to Thráin about his Ring of Power:

  LotR - Appendix A said:

  This may prove the foundation of new fortune for you yet, though that seems unlikely. But it needs gold to breed gold.

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• Moon-letters on Thorins map
• The West Gate of Moria
• Legolas ability to walk over snow.
• Elrond's healing powers
• The Morgul Blade that slowly pulls Frodo into the secondary world.
• The Voice of Saruman (his only magical power that is ever mentionend)
• Gleaming of elvish swords when orcs are near
• The mirror of Galadriel
• The Palantíri
• The elvish waybread: Lembas

Most visible "magic" effects I can think of are related to Gandalf:

• Gandalfs fireworks
• Gandalf shapes the waves of River Bruinen like white horses
• Gandalf is able to have his staff glowing
• Gandalf is great with inflaming fire wood, pine cones and even large trees (also Legolas arrow and Aragorns sword)
• Gandalf locks the door of the chamber of Mazarbul to hold off the Balrog
• When the Balrog attacks Gandalf there is a white flash and the Balrog's sword melts
• Gandalf collapses the Bridge of Khazad-dûm
• Gandalf shoots a ray of white light at the flying Nazgûl to turn them away.

Only very few mentioned magical powers of the Witch-king come into my mind.

• The Black Breath
• Every blade that hurts him decays.
• When Merry hurts the Witch-king, his arm becomes numb instantly.

When I think of the Witch-king as a sorcerer I imagine his primary power to be control over other beings. Over orcs and humans in visible world and wraiths in secondary world.