Windows scrolling on their own?

I have a Logitech M353 (not the same mouse).

In the Logitech Options, (the Logitech software you indicate is installed), go to Point and Scroll (Mouse menu is default) and turn off Smooth Scrolling.  

Does that help?

Is this a laptop? If so, go into the device manager and disable both the touch screen (if yours is touch-enabled) and also the built-in mouse (trackpad or pointer) device and see if that makes a difference. If it doesn't make a difference, then does disconnecting the external mouse change anything?

If it's not a laptop, disregard the above.

Smooth scrolling was off & this is a desktop, not laptop

The question is of course, what happens if you start the computer WITHOUT the mouse connected (remove USB dongle)? Still scrolling on its own?

Try a completely different mouse for a day or two to see if that makes a difference.

Also update BIOS, Chipset and Video drivers followed by all Windows Updates

Nobody asked so far but - since when does this happen / did you change anything like install software or update?

Assuming you have an up to date virus scanner, did you try to check for malware? You can try/check with MalwareBytes AntiMalware for example.

All started with a new mouse & KB, but same brand as before.
Will check for malware and/or any software conflicts with older versions of soft ware.

As suggested above try a completely different mouse (different brand)

Try updating the unifying driver:
https://download01.logi.com/web/ftp/pub/controldevices/unifying/unifying250.exe

and the software:
https://download01.logi.com/web/ftp/pub/techsupport/options/Options_7.12.43.exe

Please check the downloads, I selected Windows7 but they may default to Windows10 - this is the download page:
https://support.logitech.com/en_us/product/marathon-mouse-m705/downloads

User went our & bought a new MK 710 mouse & KB & all seems to be fine, now. I know he tested it out on internet, not sure about windows explorer, will hear back from him tomorrow....

And the feedback I'm getting is that scrolling problem seems to have gone away with the new mouse & keyboard.