To get child category of parent in archives

child_cat_archives.php

<?php

  $cat = get_query_var('cat');
	$category = get_category ($cat);
	
	if(is_archive()) {
	?>
	<div id="bread-cat-list-archive">
	
	<h2><?php echo $category->name; ?></h2>
	<?php
	if ($category->cat_ID) {
 
		if(!$category->category_parent) // if category has NO parent
			$children = wp_list_categories("orderby=id&depth=0&hide_empty=0&title_li=&child_of=".$category->cat_ID."&echo=0");
 
		else // if category has parent, show children of current category's parent
			$children = wp_list_categories("orderby=id&depth=0&hide_empty=0&exclude=".$category->cat_ID."&title_li=&child_of=".$category->category_parent."&echo=0");
 
		if ($children) {
			echo "<h5>More Categories: </h5>" . $children;
		}
 
	}
	?>
	</div>
	<?php
	}
}