As tab_indexer
is a ASP.NET control, you have to use Control.ClientID
In jQuery when you want elemnts to be selected using use ID Selector (“#id”), i.e. prefix id with #
Change your code as
$(document).ready(function () {
//Get tab_indexer element
var tab_indexer = $("#" + <%= tab_indexer.ClientID %> );
//Set checkbox checked with value stored in tab_indexer
$('#' + tab_indexer.val()).prop('checked', 'checked');
$("input[type=checkbox]").on('click', function () {
$(tab_indexer).val($(this).attr("id"));
});
});