Display children of the category a post is assigned to

get the category or categories of the single post with get_the_category() and loop through them, calling the child category lists if available.

<ul>
<?php 
if( is_single() ) {
    $post_cats = get_the_category();
        foreach( $post_cats as $post_cat ) {
            wp_list_categories( array(
                'child_of' => $post_cat->term_id,
                'title_li' => 0,
                'show_option_none' => ''
            ) );
    }
}
?>
</ul>