To get child categories of parent in single post.

child_cat.php

<?php

  $category = get_the_category();
	$category = get_category ($category[0]->cat_ID);	

	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");
	}