Is there any appropriate method to clear a server side session on client side. I use java script to clear a session, but when ever a page is redirected then server side session
What you can do is "Invoke a Server side page from javascript and Clear the session there".
If you are using jQuery, It is simple as this
Logout
Assumung inside the logout.aspx page load event, you are clearing the Session. You may need to update some part of your UI( Logged in user name, some liknks etc..) once the user is logged out.