Is there any facility to clear inbox message? If I want to delete some of the messages from inbox, then is it possible?
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It's not really an inbox, it's notifications of activity that is relevant to you and hence you might be interested in.
Everything you see in that 'inbox' is a public post somewhere on the Stack Exchange network. So once you've acknowledged that you've seen it (by dropping down the inbox, which clears the red dot), there's nothing more to do.
No, there is no direct way to clean those "messages" because they're not standalone - they represent some real content that exist somewhere else and only linked in the message.
The only way to have messages removed from your Stack Exchange Inbox is to delete the related posts/comments.
For example, you can flag this comment as "obsolete" or "not constructive" if you want and if moderator will remove it, the related item in your Inbox would be removed as well.
In case of answers to your question (like this one) there's not much you can do though.
If you will explain why it bothers you so much to have Inbox items maybe we can come with better answer.
To clear the glowing red dot, just view them. (Click on the glowing dot)
Otherwise, nope--no facility to clear inbox messages. Why would you want that anyway?