Did the Nazgûl retain their Rings of Power?

Question

In The Fellowship of the Rings, Frodo sees the true appearance of the Nazgûl:

He was able to see beneath their black wrappings. There were five tall figures: two standing on the lip of the dell, three advancing. In their white faces burned keen and merciless eyes; under their mantles were long grey robes; upon their grey hairs were helms of silver; in their haggard hands were swords of steel. Their eyes fell on him and pierced him, as they rushed towards him.

The Fellowship of the Ring - J.R.R. Tolkien - chapter 11, A Knife In the Dark

There's no mention of the Nazgûl wearing the rings of power that Sauron gave them, although their hands are referenced. Did the Nazgûl retain their rings of power once they became wraiths? Or did something else happen to the rings once the Nazgûl emerged?¹

¹ _{As an FYI, I am currently re-reading The Lord of the Rings trilogy and am just pages from being done with The Fellowship of the Ring. I'm very familiar with the Peter Jackson movies. So that's where I'm coming from as far as canon knowledge goes.}

Answer 1

No, Sauron held the Nazgûl's Rings.

It's mentioned in a few places:

Letter 246:

... Sauron, who still through their nine rings (which he held) had primary control. ...

The Fellowship of the Ring, when Gandalf tells Frodo,

"the Nine [Sauron] has gathered to himself; the Seven also, or else they are destroyed."

Unfinished Tales:

Sauron’s “mightiest servants, the Ring-wraiths, who had no will but his own, being each utterly subservient to the ring that had enslaved him, which Sauron held.”

...

the Ringwraiths “were entirely enslaved to their Nine Rings, which [Sauron] now himself held”.

Answer 2

Yes they wear them, from The Fellowship of the Ring Gandalf says to the council of Elrond:

The Nine [rings] the Nazgûl keep.

There are some passages that indicate that Sauron "possesses" the Nine, however some of these are from before it is known that the Nine have left Mordor, and they mostly just indicate that Sauron controls the rings, not that he actually holds them himself.

Answer 3

Tolkien was pretty clear about this in one of his letters:

Sauron sent at once the Ringwraiths. They were naturally full instructed, and in no way deceived as to the real lordship of the Ring...But the situation was now different to that under Weathertop, where Frodo acted merely in fear and wished only to use (in vain) the Ring's subsidiary power of conferring invisibility. He had grown since then. Would they have been immune from its power if he claimed it as an instrument of command and domination? Not wholly. I do not think they could have attacked him with violence, nor laid hold upon him or taken him captive; they would have obeyed or feigned to obey any minor command of his that did not interfere with their errand - laid upon them by Sauron, who still through their nine rings (which he held) had primary control of their wills...

From The Letters of J.R.R. Tolkien #246

So there you have it. Sauron kept, and held, the nine rings and the Nazgûl did not wear them.