As I understand it, silvered (PHB p. 148) and/or adamantine (XGtE p. 78) weapons or ammunition do not automatically count as magical. There is no text describing them as magical, and they are not found on lists of magic items (unlike, for example, Mithral Armor or Adamantine Armor which appear on a list of magic items in the DMG).

I mention this because the spell Swift Quiver has some text that concerning nonmagical ammunition (PHB, p. 279-280, bold added):

Components: V, S, M (a quiver containing at least one piece of ammunition)

You transmute your quiver so it produces an endless supply of nonmagical ammunition...

Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of nonmagical ammunition.

So the ammunition that is produced by this spell is nonmagical, but otherwise is "similar" to whatever piece of ammunition was just used. And the quiver starts with at least one piece of real ammunition in it (that you used as part of a material component to cast the spell, and that is not consumed in the casting). So that got me thinking:

If someone was to have a quiver that contained one silvered arrow and one adamantine coated arrow (neither of which was magical), would they then be able to use Swift Quiver to attack with silvered (or adamantine) arrows until the end of the spell's duration?

Yes.

In order to cast the spell, you must provide the following material component (from the spell description):

a quiver containing at least one piece of ammunition

If you have a quiver containing a silver arrow and an adamantine arrow, you fulfill the material component requirements of the spell. In other words, the quiver of at least one arrow (not simply an arrow by itself) is the material component.

Then, here's how the spell's effect works (from the description, emphasis mine):

You transmute your quiver so it produces an endless supply of nonmagical ammunition...

On each of your turns until the spell ends, you can use a bonus action to make two attacks with a weapon that uses ammunition from the quiver. Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of nonmagical ammunition...

Once the quiver is transmuted, each attack you make using ammunition from the quiver causes the quiver to automatically replace that ammunition with a similar sort. Since you make multiple attacks during the spell's duration, each attack with an original arrow produces a replacement arrow, which then gets used and replaced, which then gets used and replaced, and so on.

As you correctly noted, silver and adamantine ammunition are not inherently magical, so each replacement arrow will be of similar make. But, do note the following (from the description):

Any pieces of ammunition created by this spell disintegrate when the spell ends.

So once you've shot one of the original pieces of ammunition, no matter how many times you can continue to replace and shoot the replacement again for the duration of the spell, once the spell is over the original (which you've shot away) and any of its replacements (which disintegrate) will be gone. Thus if you start with only a silver arrow and an adamantine arrow and you fire both silver and adamantine arrows during the spell's duration, you'll be left with an empty quiver (unless you can recover the original arrows subject to the normal ammo recovery rules).

Yes, this should work

The spell allows you to create duplicates of any non-magical arrow in your quiver. Silver and Adamantine weapons are not magical, so the spell should work on them.

As for mixing up Silver and Adamantine arrows, I see no reason this wouldn't work as well. Swift Quiver is a spell cast on a quiver that contains at least one piece of ammunition...the phrasing implies that the target is the quiver, not the arrows inside of it. There's simply the restriction that the quiver must have at least one arrow in it to be a valid target for the spell.

Once the spell is cast...

Each time you make such a ranged attack, your quiver magically replaces the piece of ammunition you used with a similar piece of nonmagical ammunition.

Emphasis Mine.

The way this is worded, it is addressing the piece of ammunition you used to make the ranged attack. Any arrow drawn from the quiver that is fired using your spell-based Bonus Action attack(s) is instantly replaced with a copy of itself.

Ambiguity in phrasing?

To address the 'ambiguity' called out in comments...here is my rationale:

The material component for this spell is not a piece of ammunition. The material component for this spell is a quiver that must have greater than or equal to 1 piece(s) of ammunition inside of it. The target is the quiver, the qualifier is that it must contain ammo. Because you can also target a quiver that is completely full of 20 arrows.

Thus, the entire quiver is enchanted, not a single piece of ammunition that is inside the quiver. If that was the case, it would say so. Instead, the spell says that when you draw and fire an arrow using your Bonus Action, it is immediately replaced.

Note of caution

When the spell ends, all arrows created by the spell disintegrate. Because the spell replaces arrows after you draw and fire them, the first arrow you draw is not one created by the spell. So if you plan to use this with Silvered or Adamantine arrows, you may want to keep several of them in your quiver, since you will have to fire at least one real one before you can start firing magical copies.

Final Note

There are no comments from Sage Advice or other Developers weighing in on this one way or another.

Yes and no

Yes, you can make silver (or ademantine) ammunition.

No, you can’t do both at the same time. While the spell does not preclude having more than one piece of ammunition in the quiver, you have to select one to be “the piece of ammunition you used.”