AJAX PHP MYSQL值更新无法正常工作

i have this script which updates a counter in a mysql database but it's not working at all and i can't see what wrong as i am new into php and ajax:

$(function () {
        $('.press_me').click(function(){

    var button_ID= $(this).parent('tr').attr($row['ID']);
    $.post('counter.php', {button_ID: button_ID}, function(result){

          $($row['Teme_nefacute']).html(result);
        });
request.done(function( msg ) {

                                    alert('Success');
                                    return;

                              });
                              request.fail(function(jqXHR, textStatus) {
                                    alert( "Request failed: " + textStatus );
                                });
});
});

and counter.php:

    <?php
// Connection to database
  $connection=mysqli_connect("host","user","pass","db");
// Check connection
  if (mysqli_connect_errno())
    {
    echo 'NOT_OK';
    //echo "Failed to connect to MySQL: " . mysqli_connect_error();
    }

// Increasing the current value with 1
 mysqli_query($connection,"UPDATE table SET amount= (amount + 1) WHERE ID=' " . $_POST["button_ID"] ." ' ");

$get_count= mysqli_query("SELECT * FROM `table` WHERE `ID`=' " . $_POST["button_ID"] . " ' ");
$count_data= mysqli_fetch_array($new_count_data);
echo($count_data["amount"]);

  mysqli_close($connection);

  ?>

can anyone help me make it work async?

First of all, PHP is a backend technology which works in server and sends result to client (browser, curl, wget etc.) Javascript is a frontend technology which works in the client. So in that point of view

Your php code should be between of <?php //code ?> tags, and it would executed in backend then result would be printed in javascript code.

As a result your view should be a php file. But it should contain html,js and php mixed.

   <script>
    $(function () {
      $('.press_me').click(function() {

        var button_ID= $(this).parent('tr').attr("<?php echo $row['ID']; ?>");
        $.post('counter.php', {button_ID: button_ID}, function(result) {

          $("<?php echo $row['Teme_nefacute']; ?>").html(result);
        });
        request.done(function(msg) {

          alert('Success');
          return;

        });
        request.fail(function(jqXHR, textStatus) {
          alert( "Request failed: " + textStatus );
        });
      });
    });
    </script>

Your php code looks OK. When you try like this what is the result ?

Updated :

If your table name is table then please place it between this characters `` like in SELECT query. table has a special meaning in SQL.