Datepicker not supporting timepicker

WordPress supports only datepicker. If you want to add timepicker in datepicker you have to use jquery-ui-timepicker-addon as extension in your theme or plug-in.

Add css and js as below

add_action('wp_enqueue_scripts', 'custom_datepicker');
function custom_datepicker() {
    //wp_enqueue_script('jquery-ui-datepicker');
    //wp_enqueue_script('jquery-ui-core');          
    wp_enqueue_script('jquery-ui-timepicker-addon',get_stylesheet_directory_uri().'/js/jquery-ui-timepicker-addon.js',array());
    wp_enqueue_style('jquery-ui-timepicker-addon',get_stylesheet_directory_uri().'/css/jquery-ui-timepicker-addon.css',array());
    wp_enqueue_style('jquery-ui',get_stylesheet_directory_uri().'/css/jquery-ui.css',array());  
}

You can download all css and js files from this link http://trentrichardson.com/examples/timepicker/

Call timepicker as below

<script type="text/javascript">
    jQuery(document).ready(function($){
        $('#datetime').datetimepicker({
          timeFormat: "hh:mm",
          dateFormat : 'yy-mm-dd'
        });
    });
</script>

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