Trigger Drupal Custom AJAX Programmatically

// Your custom Javascript file:
(function ($) {
  $(function () {
    /**
     * Add an extra function to the Drupal ajax object that is specific to our
     * custom Drupal menu callback for: "custom/ajax/%/%".
     */
    Drupal.ajax.prototype.customAjaxHandler = function (arg1, arg2) {
      // Do not perform another ajax command if one is already in progress.
      if (this.ajaxing) {
        return false;
      }
 
      // Need to add the two url arguments.
      this.options.url = this.options.url.replace('%/%', (arg1 + '/' + arg2));
 
      try {
        $.ajax(this.options);
      }
      catch (err) {
        console.log('An error occurred while attempting to process ' + this.options.url);
        return false;
      }
    };
 
  });
 
})(jQuery);

// In your_module.module
/**
 * Implements hook_menu().
 */
function your_module_menu() {
  return array(
    'custom/ajax/%/%' => array(
      'page callback' => 'custom_module_update_callback',
      'page arguments' => array(2, 3),
      'access callback' => true,
      'delivery callback' => 'ajax_deliver', /* <----Important part */
      'theme callback' => 'ajax_base_page_theme', /* <--- Important part */
      'type' => MENU_CALLBACK,
    ),
  );
}
 
function custom_module_callback($arg1, $arg2) {
  return array(
    '#type' => 'ajax',
    '#commands' => array(
      ajax_command_replace('#element-wrapper-id-' . $arg1, "<div id=\"#element-wrapper-id-" . $arg1 . "\">some custom markup to return to the page.</div>")
    )
  );
}

new Drupal.ajax(null, jQuery(document.body), {url: '/pane_ajax/update/%/%'})
  .customAjaxHandler('arg-val1', 'arg-val2');