How to change permalink on post click on post listing page

you need to using jquery function functionality

<script>
var current_main = window.location.pathname;
var current= document.URL;
//var lastElement = current.substr(current.lastIndexOf("https://wordpress.stackexchange.com/") + 1);
var main_url = currentq+"?"+thechosenone+"="+thechosenone;
var main =  history.pushState(current,"", main_url );
</script>

by using this you can able to append the url’s with specified get methods.
I hope this will help you