Would you please do this :

Go to the Firefox menu (≡) => Add-ons => Extensions

( Mac  : Command + Shift + A)

and look for any other unfamiliar or suspicious looking extensions.

When you find any : remove them.

Do the same here : for Windows => Control Panel for Mac and Linux => System Preferences

However : most malware will be 'hiding' somewhere , so let's run malware scans (even though you already have run some) :

Further information can be found in this article : https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed malware scanners. They all work differently - what one program doesn't pick up, the other might.

Also see : https://malwaretips.com/blogs/remove-videojosmooth-com/

https://quickremovevirus.com/how-to-remove-videojosmooth-com-pop-up-solved/

Especially for Mac : https://www.malwarebytes.com/mac/

And : https://malwaretips.com/blogs/remove-mac-os-x-virus/

Also, Go to the Mozilla Add-ons Web Page {web Link} (There’s a lot of good stuff here) and search for a good ad / pop-up blocker.

FredMcD said

Also, Go to the Mozilla Add-ons Web Page {web Link} (There’s a lot of good stuff here) and search for a good ad / pop-up blocker.

This would be your best choice :

https://addons.mozilla.org/en-US/firefox/addon/ublock-origin/

If you think those notifications are coming from a website you visit regularly:

While viewing the site, click the left end of the address bar where you usually find the green lock or i-in-a-circle to view the drop-down. It will indicate whether the site has permission to show notifications. You can revoke the permission there if it does.

Or to view your notification permissions in one place:

• Mac: "3-bar" menu button (or Firefox menu) > Preferences
• Windows: "3-bar" menu button (or Tools menu) > Options
• Linux: "3-bar" menu button (or Edit menu) > Preferences
• Any system: type or paste about:preferences into the address bar and press Enter/Return to load it

In the left column, click "Privacy & Security"

On the right side, scroll down to the Permissions section. To the right of "Notifications, click the "Settings" button. This should open a box listing all the site-specific notification permissions that you've granted ("Allow") and sites you've denied permission ("Block"). You also can edit or remove them here.

There's also a "do not disturb" checkbox to block website notifications for the rest of your session (until you quit Firefox). You could try that as a test to see whether it stops these notifications. If not, then an add-on is the most likely culprit.

Any progress?

Thank you everyone for your help!

I'm really not a computer guy and had difficulties following your kind solutions. But meanwhile the problem seems to have solved itself – I no longer get any annoying pop-up messages and am again a happy user of Firefox.

Thank you all kind and helpful people!

Let us know if you need any more help.