<div class="custom-select">
  <ul>
    <li data-value="1" class="selected"><i class="fas fa-check"></i> Seçenek 1</li>
    <li data-value="2"><i class="fas fa-times"></i> Seçenek 2</li>
    <li data-value="3"><i class="fas fa-heart"></i> Seçenek 3</li>
  </ul>
  <input type="hidden" name="custom-select" value="1">
</div>

$('.custom-select ul li').click(function(){
  $('.custom-select ul li').removeClass('selected');
  $(this).addClass('selected');
  $('.custom-select input[type="hidden"]').val($(this).data('value'));
});