I have a Apple M4 MacBook Pro running Sequoia. I need an external DVD drive. Suggestions?

Almost any drive out there should work.

What exactly happened when you used the Verbatim and POTVMOSL drives?

Do note, for the drive to appear on the Mac, there needs to be a readable disc in it and the "CD & DVD drives" settings need to be turned on in the Finder Settings for The SideBar and Desktop (under General).

Also, the drive needs to be connected directly to the Mac via an adapter or through a powered hub.

They won't work if the hub is powered by the Mac, or the adapter is not compatible.

I use this one with my M1 MacBook Air and it works fine.

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Also note, if the drive is a Blu-Ray drive, the blu-ray portion will not work without extra software to read and / or write Blu-ray Discs. The DVD and CD portions should work directly though.

You can go to System Settings ➜ General ➜ About ➜ System Report.

The drive should appear under Disc Burning (and under USB if it's connected directly) if its correctly detected, even with no disc inside.

You may need to go to File, Refresh Information to get it to show though.

If it shows up there, but no disc appears in Finder, it normally suggests the disc is not readable in Sequoia, try a different disc.

Connect the drives and check in Disc Utility and see if they are visible. They might be formatted or have proprietary formats or security features. If Disc Utility can see them then re-format them as AFPS.

If you're connecting through a USB-A to USB-C adapter then try a different one, especially if it's not an Apple one.