Filtering the list of categories is pretty easy.
To retrieve only categories child of a specific one, proceed as follow:
- log into wordpress
- go to ‘categories’
- click on ‘edit’ for the category you consider as top one
- in the url, check the value of “tag_ID“, this is your category id (22 in this example)

- in your code, where you are making a call to “wp_list_categories()” simply add the “child_of” argument as follow:
wp_list_categories("child_of=$your_top_category_id");in this example: wp_list_categories(‘child_id=22′);
- that’s it!
Additional customization is possible since a bunch of configuration variables (including category nesting, number of posts in a category, …) are available as defined here: http://codex.wordpress.org/Function_Reference/dynamic_sidebar