I presume you are using IMAP.

Try: access webmail account and set up a filter to move incoming specified emails from Inbox to a suitably named folder.

then in Thunderbird subscribe to see that particular folder. then set it to synchronise that subscribed folder so you get a copy downloaded to your Thunderbird profile.

If you get additional email addresses you would need to add them to the filter.

Thanks for your reply . Yes I am using IMAP . I cant understand your words " access webmail account " . Is it possible the selected emails (with respect to senders email address) from Gmail inbox load to thunderbird ? . What is the role for webmail here .

Thunderbird will, like other email clients, simply collect for you what arrives in the account's mailbox. So if you can get the server to put these particular messages aside for you in your own folder (for which you'd normally go to the webmail site offered by your email provider) you can set Thunderbird to look only at your own folder and it won't need to handle what's in the common Inbox.

Webmail:

When you created a gmail account, you were able to access it via a browser using an internet connection.

You can access the gmail/google account by using a browser eg: Mozilla Firefox. https://accounts.google.com/ServiceLogin?