horizontal colored lines appearing after saving a PSD in PS

i see your point, but the Mac is new, the HD and cable are one-day new, I don't disconect them ever and I don't touch them while working on them...

Until now.

It's not that it doesn't work. It's that the risk of file corruption is very much higher. And that's what just happened to you.

The problem isn't the disk itself. It's cables and connectors. The drive is constantly connected and disconnected, it is moved and bumped around, and it's inevitable that the connectors become looser over time. A save is much more complex operation than a simple transfer, taking more time. All this increases corruption risk.

It only takes a nanosecond broken connection for a file to become corrupted.

If you absolutely have to work off external drives, prioritize. Move things off your system drive and over to the external, rather than leaving it, forcing you to work directly on the external. Take your precautions. Make sure the connectors fit firmly. Replace all cables at regular intervals. Do not touch the drive when transfer is in progress! Walk away until it's finished.

yes, formatted the new SSD yesterday as soon as I connected it to the Mac.
I just can't imagine how could I work on the photos dragging them back and forth from the external to the interior HD everytime I need: it would slower all the process, mess with the LR catalog and be a huge risk of chaos in handling the files.

I shoot tens of Gb every week, and keep projects "under-construction" for weeks. I need to have the files on a big enough HD and be able to work on that same HD. 
I've been working on external hard disks for years, I know tens of photographers who do so, and nobody ever encountered this problem...

What you should be doing is storing everything on the external, then dragging over to local to edit, then drag back to the external when completed. Not working directly off the external.

@paolofus did you reformat the external drive to Mac Compatible?

NEW UPDATE: I bought just yesterday a new external SSD, because the storage space on the Mac HD is too small, hoping the problem was with the old SSD.

Today, I already got the first image with an horizontal colored banner...

I've started to work only on the mac HD, not on the external SSD, and that seems to have solved the issue.
the colored lines only appear when i close the fine, after saving, and open it on LR. But again, as many has pointed, it could be a working-on-external-drive issue

As you may have read I'm facing the same issue. But I have one question: while working on your file I guess you save every now and then. Has it ever occurred while you are saving or the line only appears once you save AND CLOSE the file? Because this exactly is what happens to me. The colored line appears only after I close the file. I mean, for the rest, my external ssd works fine and this makes me wonder whether it is actually a hardware issue or not.

What we can say for certain right now, is that file corruption is always caused by failing hardware.

External drives is high up on that list. It doesn't have to be the drive itself - frequently overlooked is worn cables and connectors. It only takes a nanosecond broken connection. Don't move or even touch the drive while it's writing.

That's actually what I'm doing right now. The thing is that it happened just 3 times the last couple of months. So I'm gonna have to save locally from now on to reach to a conclusion in the next month or so .