How to catch click in wordpress menu item

Solution:

It seems that your jQuery code is targeting the <li> element instead of the actual link. A slight correction to target the <a> element might do the trick here:

(function($) {
 $(document).ready(function() {
     $(document).on('click', '.custom-menu-button a', function(event){
       alert("caught");
     });
   });
})(jQuery);