Is this account POP or IMAP?

If it's IMAP and the annual backups are also on the server then they will count towards your quota. We'd have to get clear whether the error messages means specifically your Inbox, or your whole account.

In it's a POP-connected account, are you sure you have removed messages from the server?

Do you compact regularly?

In either case, moving your archive to Local Folders in Thunderbird may be the most useful thing to do.

It's a POP-connected account,Yes i compact regularly. You are correct sir, the error messages is coming to whole account.

Do you keep any messages on the server? You would need to logon to webmail account via a browser to see how many emails are actually on the server. Empty the Spam folder on the server. Are there any new emails on the server that are not downloading? If there are only a few emails and new emails not downloaded to Thunderbird, what happens if you do this:

In thunderbird

• Move all good emails out of Inbox into other suitable folders for organising.
• Delete all unwanted mail.

When Inbox is empty:

• right click on Inbox and select 'Compact'.

• right click on 'Junk' and select 'Empty Junk'
• right click on 'Junk' and select 'Compact'

• right click on 'Deleted' and select 'Empty Deleted'.

Note 'Deleted' folder might be called 'Trash'

As per your instruction i have logged to webmail account> There i was made folder called 2015 and there are so many mails. I think i was forgotten to delete these mails but now i have deleted all the mails from that folder. Sir the above error is coming due to this?? Now i will check.

In thunderbird

  I have made year wise folders and moved all mails to that folder. But now i have kept only 2016 years mails and deleted folders of 2014 and 2015 from original mail folder, again if  copy same folders in the original mail folder then mail box full message is coming and new mails are not coming.