Does this happen prior to adding an account? On only after having done so? What is exact wording of the message?

It's so frequent it's hard to tell, but probably after I have added an account.

The pop-up says: Password Required - Mozilla Thunderbird.

That means that the account is requesting via thunderbird the password to confirm that the account belongs to you.

I do appreciate your fast response David. But I'm still having a problem.

On opening Thunderbird I get a white screen with the attached.

If I click on cancel, I can add another account, which Thunderbird finds, but on clicking done. I'm asked for the password again, so I add the password for the account I am trying to add, but no go. The same pop up arises again.

And thereafter the popup keeps appearing. So sorry to say I'm still stumped.

I think I fixed the problem David. And I share this for anyone else who might be having a similar problem.

I came across this: https://support.mozilla.org/en-US/kb/protect-your-thunderbird-passwords-primary-password

And using the information I was able to access the password information by inputting a code, which led to a pop up that showed I had no password and where I was able to add a password.

I don't know if I missed something in the startup of Thunderbird, which is always a possibility being clueless on these things, but all's well that end's well. I now actually do have a password that allows me access and to add more accounts.

I do thank you for your help. May your week be wonderful.