How to show only child_of for parent?

My archives pages are only showing one child category at a time. I’d rather have them show all the child categories within the parent category.

I found the “child_of” parameter, but not sure where to place it in my code. Each child category only has one post assigned to it. The reasoning is as follows: browse by brand > brands > product.

My site is https://www.ammunitionstorage.net/category/by-brand/

My code is:

<ul class="wpn_archives">
<?php while (have_posts()) : the_post(); ?>
<li>
<img class="wpn_thumb" src="<?php echo get_post_meta($post->ID, "thumbnail", true); ?>" alt="" />
<!--<a class="wpn_comments" href="<?php the_permalink(); ?>#comments"><?php comments_number('0', '1', '%'); ?></a>-->
<h2><a href="<?php the_permalink(); ?>"><?php category_title(get_the_title()); ?></a></h2>
<span>Product inventory is continuously updated</span>
<!--<span>Published on <?php the_time('l, F j, Y') ?> by <?php the_author_posts_link() ?></span>-->
<!--<?php wpn_content_show(370); ?>-->
<a href="<?php the_permalink(); ?>">Read More &raquo;</a>
</li>
<?php endwhile; ?>

The “by brand” is only one such category, so I need all parent categories to show their children.

Any help is very much appreciated.