Test if a page has children or not

wp_has_children_pages.php

<?php 
	$parent_ID = $post->post_parent ? @ array_pop(get_post_ancestors($post)) : $post->ID;
	$children = wp_list_pages(
		 array(
			 'child_of' => $parent_ID,
			 'title_li' => '',
			 'echo'		=> false,
		 )
	);
?>
<?php if ($children) : ?>
	<h3 class="widget-title"><?php _e('Read also in this section', 'textdomain'); ?></h3>
	
	<?php if ($post->post_parent) {
		$children = wp_list_pages(array(
			'depth'      => 1,
			'title_li'   => '',
			'child_of'   => $post->post_parent,
			'echo'       => 0
		));
	} else {
		$children = wp_list_pages(array(
			'depth'     => 1,
			'title_li'  => '',
			'child_of'  => $post->ID,
			'echo'      => 0
		));
	}
	?>
	<?php if ($children) : ?>
		<ul>
			<?php echo $children; ?>
		</ul>
	<?php endif; ?>
<?php endif ?>