.fail(function(jqXHR, textStatus, errorThrown) {
    console.log('fail: ', textStatus, errorThrown);
})

.fail(function(jqXHR, textStatus, errorThrown) {
    console.log('fail: ', textStatus, errorThrown);
})

fail:  error Internal Server Error

$(document).ready(() => {
    $(function() {
        $('#quote_form').submit(function(e) {
    $.ajax({
        url: 'sendmail.php', 
        type: 'POST',
        data: $("#quote_form").serialize(),
        success:function(responseAnyNameHere) {
          $('.responseArea').html(responseAnyNameHere);
        },
        statusCode:{
          404:function(){
            //$('.error').html("Page not found!");
            alert( "file not found" );
          }
        }
      }).done(function() {
      alert( "success" )
      }).fail(function(jqXHR, textStatus, errorThrown) {
console.log('fail: ', textStatus, errorThrown);
})
.always(function() {
      alert( "complete" );
    });
          //отмена действия по умолчанию для кнопки submit
          e.preventDefault(); 
        });
      });
    });