Synchronization & Storage is an IMAP option. POP does not provide syncing.

Log in to webmail and check your account's POP settings. Change them so that ALL messages can be downloaded regardless of age.

Hi,

I just checked. There is no such POP settings to download all messages regardless of age.

I am using rediffmailpro. Is there any other way?

Your provider has IMAP settings according to https://businessemail.rediff.com/faq/email/102.html

Thank you for the IMAP configuration. I followed the instructions. But it is not downloading all messages, just for a week or two. I have selected option to download all messages under Synchronization & Storage.

Any pointers?

Then something is very wrong with your account and you need to contact your provider. Using IMAP, you should see the exact same messages and folders in Thunderbird, as those you see via webmail. Do you see all your messages in webmail?

By default I can’t see all mails in webmail. I need to click on the show more button which shows next 30 or 40 mails. I have to click that button multiple times if I want to go further down the date.

I guess, I need to contact the service provider to show all mails without clicking buttons.

What you should be contacting your provider for, is the fact that you can't access all your messages via IMAP or POP.