post meta data: display the child category from one parent only

To give an example, one of the Parent categories is “Author”, and its child categories are “author-1”, “author-2”, “author-3” etc. I want only the child category “author-x” to be displayed.

Well author-x isn’t your choice. Which of those three do you want?

Also, is it always the Author category that you are wanting this? Or are there other Parent/child categories that must be dealt with?

Thank you for the reply.
Yes I only want to list the author. The other parent/child categories will be dealt with elsewhere..
The list of child categories mentioned above(“author-1” etc.) was said as an example. They are not the actual names! Maybe I didn’t explain it very well…

Each post will be filed under an author. Its parent category is called “Author”. So I want to have the author name(child of “Author”) displayed on it’s own, excluding the other parent and child categories associated with the post(“Book Title”, “Publisher” etc).
By default the_category() lists all categories and I don’t want this.
Any ideas or useful links would be appreciated.

So you want only the Category displayed if it is a child of “Author”?

<?php
//get categories for this post and only display if the category parent is Author
$author_cat=get_cat_ID('Author');
$categories=get_the_category();
  foreach($categories as $category) {
    if ($category->parent == $author_cat) {
        echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
    }
  }
?>

Wow thank you so much for this! The title text also. You have made my day ??