Esta pergunta já tem uma resposta aqui:

Quando eu cliquei no link do livro, ele recarrega a página e classifica a coluna. Eu quero parar a recarga usando ajax ,,, Como?

estas são as minhas funções neste processo.

esta função getBook

public function getBooks($start = 0, $limit = 2, $order = "ASC")
{
   $sql_start = $start * $limit;
   $sql_limit = $limit;
   $sql_order_by = $order;

   $query = "SELECT Library.nameOfBook, userBook.book_id, userBook.user_id FROM loginUser JOIN userBook JOIN Library ON userBook.user_id = loginUser.id AND userBook.book_id = Library.id WHERE loginUser.username=:username ORDER BY Library.nameOfBook $sql_order_by LIMIT $sql_start, $sql_limit";
   $statment = $this->db->prepare($query);
   $statment->execute([
       ':username' => $this->username
   ]);
   $result = $statment->fetchAll();

  echo "<table id='myTable' border='1'>

  <tr>
   <th><a id='sorter' href='#'>Books</a></th>
   <th>Action</th>
   </tr>";
   foreach($result as $row){
       echo "<tr>";
       echo "<td>" . $row['nameOfBook'] . "</td>";
       echo "<td>" ."<input type='submit' id='delete".$row['book_id']."-".$row['user_id']."' onclick='deleteBook(this)' name='delete' value='Delete'>" . "</td>";
       echo "</tr>";
    }

   echo "</table>";
   echo "";
   return count($result);
 }

esta função jquery

<script>
  $(document).ready(function() {
  $( "#sorter" ).click(function() {
    var order_by_value = $('input[name="order_by"]').val();
    if(order_by_value == "ASC"){
        $('input[name="order_by"]').val("DESC");
    }
    else {
        $('input[name="order_by"]').val("ASC");
    }
    $('input[name="current"]').trigger('click');
 });

 });
</script>