If you were copying the files, then the originals should still be on the source drive.
If @TheLittles' first two suggestions don't work, but the USB stick is physically seen by macOS, then the next step would be to make a raw bit for bit clone of the drive. The command line utility "dd" can be used, but GNU ddrescue works better if the drive has physical issues. By cloning the USB stick and working from the raw image or the clone you don't further degrade the USB stick if you need to use a professional data recovery service such as Drive Savers or Kroll Ontrack both of which provide free estimates. You have to be extremely careful with these utilities since it is very easy to overwrite the data you are trying to recover.
PhotoRec and TestDisk are two free multi-platform utilities (Mac/Windows/Linux) for recovering data from a drive depending on the file system used on the USB stick. I've had TestDisk correct file system issues on a corrupt drive/image in order to allow the transfer of a file. TestDisk works without mounting the volume. You should work from the clone just to be safe since it is very easy to make a mistake.
Data Rescue is a paid app I used years ago.
Sometimes Disk Utility is needed to repair a file system even on the clone, but sometimes Disk Utility is unable to repair the drive and Disk Warrior may be needed to get the file system in state where the drive can be mounted.
There is no guarantee any app will be able to read or recover data from a USB stick. If cloning the drive and using the free apps don't work, I think it would be best to consult one of the professional data recovery services I mentioned earlier instead of spending/wasting money on apps that may not work.
If you might use a professional data recovery service, then please minimize doing anything beyond trying to use Disk Utility First Aid on the USB stick. If the data is critical, then don't even make any further attempts to mount the drive (or use Disk Utility) and consult a professional service so you don't make their job harder or even impossible.