As per my app requirement
Please suggest me the way to achive the functionality along with any useful libraries of java
If we want a long lived connection to the twitter streaming api, you're right. Appengine is not a good use case.
However, there is nothing stopping you from spinning up a VM or Cluster on compute engine to handle the streaming traffic from twitter. From there your VM or cluster can communicate with your appengine project and do what you need to do with the tweets.
In regards to libraries or code your on you're own for that part of this, but that's the approach I would take.