test

HTML

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<table>
  <tbody>

    <tr>
      <td>
        <div class="custom-control custom-checkbox">
        <!--added class here-->
          <input type="checkbox" class="custom-control-input check_amount">
          <label class="custom-control-label" for="check_amount">1</label>
        </div>
      </td>
      <td name="selected_fees">
        fee 1
      </td>
      <td name="amount">
        123
      </td>
      <td>
        A
      </td>
    </tr>
    <tr>
      <td>
        <div class="custom-control custom-checkbox">
          <input type="checkbox" class="custom-control-input check_amount">
          <label class="custom-control-label" for="check_amount">1</label>
        </div>
      </td>
      <td name="selected_fees">
        fee 2
      </td>
      <td name="amount">
        12
      </td>
      <td>
        fee 3
      </td>
    </tr>

  </tbody>
</table>

<div class="form-group">
  <label for="tp">Total payment</label>
  <input type="number" class="form-control" id="tp" name="tp" required disabled>
</div>
<div class="form-group">
  <label for="fs">Fees selected</label>
  <input type="text" class="form-control" id="fs" name="fs" required disabled>
</div>

JavaScript

$(function() {
  $(".check_amount").click(function(event) {
    var total = 0;
    var name = "";
    //loop through checked checkbox
    $("tbody input[type=checkbox]:checked").each(function() {
      total += parseInt($(this).closest('tr').find('td[name=amount]').text().trim()); //get td value
       name += $(this).closest('tr').find('td[name=selected_fees]').text().trim() + " "; //get td value
      
    });
    alert(name)
    $('#tp').val(total);
  
    $('#fs').val(name);
  });
  
});