$(document).ready triggers the first time when the DOM loads. So at that time there is only one node and event id bind to that node. When new node is added, the change event is not added with $(document).ready. You have to bind that namually as I did in your $('#sigepapa').click listner.

Also you have to have independent inputs for each and every select tags that were present initially aswell as created with clone. So rather than selecting element with id using $('#ahh'), you could use ahh as the classname. Because these elements will be present more than one time. Id is supposed to be unique, so better use class for this purpose.

This node can be selected on change of the select tag as the next element of the select. This select can be recieved using event.target from change event. That particular element will be $(e.target).next('.ahh') in this scenario

Working Fiddle

$("#sigepapa").click(function () {
  var ako = "";
  ako += '<select class="handicap">';
  ako += '<option value="a">Example 1</option>';
  ako += '<option value="b"> Example 2</option>';
  ako += "</select>";
  
  ako += '<div class="ahh">';
  ako += '<div class="row">';
  ako += '<div class="inputs">';
  ako += "</div>";
  ako += "</div>";
  ako += "</div>";

  $("#ugh").append(ako);
  bindEvents();
});

function bindEvents() {
  $(".handicap").change(function (e) {
    var val = $(this).val();
    if (val == "a") {
      $(e.target).next('.ahh').html(
        '<div class="row"><div class="inputs"><input type="text" name="mc" class="ja"></div></div>'
      );
    } else {
      $(e.target).next('.ahh').html(
        '<div class="row"><div class="inputs"><input type="text" name="cb" class="ja"></div></div>'
      );
    }
  });
}

$(document).ready(function () {
  bindEvents();
});

<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.5.1/jquery.min.js"></script>
<div id="ugh">
  <select class="handicap">
    <option value="a">Example 1</option>
    <option value="b">Example 2</option>
  </select>
  <div class="ahh">
    <div class="row">
      <div class="inputs"></div>
    </div>
  </div>
</div>
<a id="sigepapa" class="fa fa-clone">Clone</a>

your onchange event is bind with old elements so it didnt work with newly added elements there is a way to handle this situation try this change and let me know if this helps in your situation

$(document).ready(function()
{
// edited line
 $('#ugh').on("change",".handicap",function()
 {
  var val = $(this).val();

  if(val == 'a')
  { 
   $('#ahh').html('<div class="row"><div class="inputs"><input type="text" name="mc" class="ja"></div></div>');
  }
  else 
  {
   $('#ahh').html('<div class="row"><div class="inputs"><input type="text" name="cb" class="ja"></div></div>')
  }
 });
});