I have a problem in my code because I want fetch both parent category and child category simultaneously but it did not work

<p class="admin-estate-add-section-input">
   Parent category
 </p>
 
 <option value=""<?=(($parent == '')?' selected':'')?>>
 <?php while($p = mysqli_fetch_assoc($parentQuery)): ?>
 <option value="<?=$p['id'];?>"<?=(($parent == $p['id'])?' selected':'')?>><?=$p['category'];?>
 <?php endwhile; ?>
 
 <br>
 <br>
 <p class="admin-estate-add-section-input">
    Child category
 </p>
 
 <br>
 <br>

function get_child_options(selected){
 if(typeof selected === 'undefined'){
 var selected = '';
 }
 var parentID = jQuery('#parent').val();
 jQuery.ajax({
 url: '/tartalomkezelo/admin/parsers/child_categories.php',
 type: 'POST',
 data: {parentID : parentID, selected: selected},
 success: function(data){
 jQuery('#child').html(data);
 },
 error: function(){alert("Something went wrong! Can't select category.")},
 });

 }

 jQuery('select[name="parent"]').change(get_child_options);

<?php
require_once $_SERVER['DOCUMENT_ROOT'].'/tartalomkezelo/core/init.php';
$parentID = (int)$_POST['parentID'];
$selected = sanitize($_POST['selected']);
$childQuery = $db->query("SELECT * FROM categories WHERE parent = '$parentID' ORDER BY category");
ob_start(); ?>

 <?php while($child = mysqli_fetch_assoc($childQuery)): ?>
 <option value="<?=$child['id'];?>"<?=(($selected == $child['id'])?' selected':'');?>><?=$child['category'];?>
 <?php endwhile; ?>
<?php echo ob_get_clean(); ?>

jQuery('document').ready(function(){
 get_child_options('<?=$category;?>');
 });