Display subcategories on each category page wordpress

Question

I created this categories structure in my wordpress:

* Category1
    * SubCategory1(of Category1)
    * SubCategory2(of Category1)
* Category2
    * SubCategory1(of Category2)
* Category3

I need to list on each category its subcategories.(without any post) So when I will access the Category one -> I should see only the subcategories. If the Main category does not have any subcategory -> I should see its posts.

My question1: What is the category page file name on wordpress? (I searched a lot but without any clear answer).

My question1: How to display for each main category(eg: Category1) only its children.

Answer 1

Add on category.php page

 <?php
    if ( is_category() ) {
      $current_cat = get_query_var('cat'); ?>
<ul> 
   <?php wp_list_categories('&title_li=&show_count=1&child_of='.$current_cat); ?>
</ul> 
   <?php  } ?>

http://codex.wordpress.org/Template_Tags/wp_list_categories

for taxonomy get sub category list taxonomy-producttax_category.php:

 <?php $args = array(
            'show_count'         => 1,
            'child_of'           => get_queried_object()->term_id,
            'taxonomy'           => 'private_category', //define your taxeonomy
            'title_li'           =>'',
        ); ?>
        <ul>
         <?php wp_list_categories( $args ); ?> 
        </ul>

Answer 2

you can achieve that with this code:

<?php
  if (is_category()) {
    $this_category = get_category($cat);
  }
?>
<?php
  if($this_category->category_parent)
    $this_category = wp_list_categories('orderby=id&show_count=0&title_li=&use_desc_for_title=1&child_of='.$this_category->category_parent."&echo=0"); else $this_category = wp_list_categories('orderby=id&show_count=0&title_li=&use_desc_for_title=1&child_of='.$this_category->cat_ID."&echo=0");
 if ($this_category) { ?>
   <ul>
     <?php echo $this_category; ?>
   </ul>
<?php } ?>