If make a category called, let's say "XXX," then add the add "XXX" to only private posts the category won't appear in your category widget.
You have two choices to access a list of your private posts.
1. Make a link in a text widget to the XXX category. It will look something like this:
You can name the link whatever you like—something folks would be uninterested in—and even if readers happen to click it, there will be nothing to see. But if you are logged in as an admin you will see your private posts.
2. Make one single post and add the "XXX" category to it.
Your readers will see that post, but won't be able to see the private posts. While you are logged in as admin however you should be able to see the private posts.