JSFiddle - React, Tailwind, and code Playground

HTML

<link rel="stylesheet" href="http://ajax.googleapis.com/ajax/libs/jqueryui/1.8.16/themes/base/jquery-ui.css" type="text/css" media="all">

date (without year) <input type="text" id="datepicker" class="DateTextBox NoYear">

<br />
date 1: (With year) <input type="text" id="datepicker1" >
<br />
date 2: (Without year) <input type="text" id="datepicker2" class="DateTextBox NoYear">

CSS

.NoYearDatePicker .ui-datepicker-year
{
 display:none;   
}

JavaScript

$('.DateTextBox.NoYear').datepicker({
            beforeShow: function (input, inst) {
              inst.dpDiv.addClass('NoYearDatePicker');
            },
            onClose: function(dateText, inst){
                inst.dpDiv.removeClass('NoYearDatePicker');
            }
        });

$('#datepicker').datepicker( { changeYear: false, dateFormat: 'dd/mm',});


$('#datepicker1').datepicker( { changeYear: true, dateFormat: 'dd/mm', });

$('#datepicker2').datepicker( { changeYear: false, dateFormat: 'dd/mm', });