JAVASCRIPT

add parameter to url without reload jquery

var refresh = window.location.protocol + "//" + window.location.host + window.location.pathname + '?arg=1';    
window.history.pushState({ path: refresh }, '', refresh);

add parameter to url without reload jquery

window.history.pushState("object or string", "Title", "new url");

add parameter at the end of url from jquery with refreshing

window.history.replaceState(null, null, "?arg=123");