Sometimes when you divide up your WordPress content into categories it all ends up in sub-categories of one or two main categories that don’t have any content themselves.
With the widget you can add a list of sub-categories even if the parent doesn’t have posts.
You can display and filter sub-categories in various ways:
<ul>
<li>Use the parent category as the widget title</li>
<li>Show post counts in bracket next to the name</li>
<li>Hide empty sub-categories</li>
<li>Add a link to the parent category to the widget title</li>
<li>Show the full sub-category tree so it include sub-sub categories and so on as well</li>
<li>Display the list as dropdown rather than as links</li>
<li>Use the first category of the current post as the parent</li>
<li>Exclude one or more sub-categories from the list</li>
<li>List the categories in reverse order</li>
</ul>

Sub Categories Widget

This Widget lists the sub-categories for a given category.

nasznjoka

Show Category parents and sub categories of the same parent of the current post/page’s category on the sidebar of a single post or a page or an archive, highlight the current subcategory the post is in 
and unlike most of similar plugins out there, this one shows where the user is from, where he/she is and where to go 
this is helpful for navigation and the overall user experience. Inspired by the problem i was facing when doing a client’s site and i think many of you 
out there meet the same challenges

Category Family Tree

Show Category ancestors and sub categories on the sidebar

Sub Categories Widget vs Category Family Tree