Display only first level children of my custom taxonomy categories

Try the following code:

$taxonomy_name="listing_category";
$queried_object = get_queried_object();
$term_id = $queried_object->term_id;

$termchildren = get_terms( $taxonomy_name, array( 'parent' => $term_id, 'hide_empty' => false ) );

echo '<ul>';
   foreach ( $termchildren as $child ) {
       echo '<li><a href="' . get_term_link( $child, $taxonomy_name ) . '">' . $child->name . '</a></li>';
   }
echo '</ul>';