How can i add ajax button to refresh new content in views pages or block. like new tweets in twitter's timeline.
You can use Views Auto-Refresh module..
Project page says
A module to refresh a view after a specified time interval. Includes advanced options to avoid reloading the whole view, and to avoid causing a full Drupal bootstrap at each refresh.
Suitable for usage on liveblogs, activity streams, comment lists, and any other view where new items are frequently added.
I guess that you don't need any button to refresh the view, every refresh it's cache clear for you unless I'm wrong.
So check if in the twitter's block settings (or view settings) there are any advanced options to say "don't cache" as you can have always fresh contents.
Let me know if it helps.