How can I only display links from a child category

your code may look like

<?php
$category = get_the_category();
foreach( $category as $cat):
  if($cat[0]->parent == ' your_parent_category_id ( Premium )'){
   echo '<a href="'.get_category_link($cat[0]->term_id ).'">'.$cat[0]->cat_name.'</a>';
  break;
  }
endforeach;
?>