Running first aid on an external disk results in errors that cannot be fixed even in recovery mode in OS Sierra?

It's not a problem unless you intend to boot from that volume. Even then it still might not be a problem.

Fixing the partition map will require erasing it. However...

It stated that there was an input output error and so immediately I suspected there may have been corruption in the drive because I had received an error while tried to create a .tar file earlier.

That's correct. I/O errors indicate that disk should no longer be considered reliable. You can erase the disk but those errors will become more frequent until it's essentially unusable. That is probably the reason the partition map became corrupted in the first place.

(NTFS format using Paragon to read it)

That is an important little detail. A sudden power interruption cannot corrupt Mac HFS+ formatted volumes, but I have no idea what that would do to an NTFS formatted volume. If that error occurred on a Mac journaled volume it would imply a physical problem. NTFS, who knows.

It's probably fixable by reformatting it, unless you know of a Windows PC utility that can fix a corrupted partition map without erasing it.

proconverter wrote:

Thanks for the reply. The errors didn't seem to occur until I unplugged the drive (NTFS format using Paragon to read it) without properly ejecting it. Are you saying that there are physical problems that exist that a complete reformat will not be able to solve? In other words, should I just throw the drive away?

FWIW, I don't believe Paragon would load while in recovery mode so First Aid would not be able to write to the drive in order to fix it.