show subcategory in page each category

Use the Menus screen under Appearance in your admin area. Expand the Categories item and pick the desired category, then click Add to menu. For sub-menus, after the item is added to the menu, drag it around until it will drop into the right place.

Also see Appearance Menus Screen.

you can create a function for it and display it everywhere you want.
here’s a start for you:

<?php
  if (is_category()) {
  $this_category = get_category($cat);
  if (get_category_children($this_category->cat_ID) != "") {
    echo "<h1>Subcategories List</h1>";
    echo "<ul>";
    wp_list_categories('orderby=id&show_count=0&title_li=
&use_desc_for_title=1&child_of='.$this_category->cat_ID);
    echo "</ul>";
  }
}
?>

This code will display a headline (Subcategories List) and then will create a ul list of the subcategories for the current parent category.