Is it possible to know the number of tweets tweeted by a user in certain period of time using twitter4j. If it is not possible to do that, are there any other APIs which can solve this problem.
Yes you can, by fetching the entire timeline of the user. Once you've got that done, you can filter the Statuses by the createdAt property.
Be careful that Twitter4j has many rate limitation, so it is possible that you won't manage to fetch all the statuses at one time.