I am using Thunderbird mail client for gmail accounts. Its works fine, enjoying functionality too. I have problem with this mail client. In client inbox it has a list of unread mails and once viewed it becomes read mail. That's not happening on the gmail servers. If I login to gmail I'm still finding unread mails which I read in Thunderbird.
Please help me how to solve this problem. Is there any option or settings or add-ons which change status of mail when I read it?
Sounds like you setup Thunderbird to use POP to get your email instead of using IMAP. If you go into Gmail and go Settings -> Forwarding and POP/IMAP there is instructions on how to setup an external mail client, like Thunderbird, to use IMAP to get your emails. Just enable IMAP access, and click the link for configuration instructions. There is a section explaining how to setup IMAP access in Thunderbird. In using IMAP, as you read email in Thunderbird, it will be marked as read in Gmail.
Most email services these days allow IMAP access through external clients. POP is good for just getting messages quickly, but IMAP allows the client to pass data back, as well (at least in the case of Gmail) as pull over folders, calendars and notes to your client.