Hi buddy,

Try this:

Code: 
<?php
       foreach((get_the_category()) as $childcat) {
              if (cat_is_ancestor_of($categoryid, $childcat)) {
                     echo '<a href="'.get_category_link($childcat->cat_ID).'" title="See more in '.$childcat->cat_name.'">';
                      echo $childcat->cat_name . '</a></li> ';
              }}
?>
Hope it helps!