ajax call to controller function outside root

The url you use is exactly like a normal link url, index.php will pick it up and convert it to wherever you application root is or follow any routing rules etc

PHP Code:

url: '<?php echo site_url('auth_public/editabout'); ?>', 


Alternatively you can hard code it in if your js is not contained in a view. Or you can set your base_url in a data attribute somewhere are read it in.