how can i use wp-ajax in wp-admin root protected for public users?

i have locked my wp-admin root folder by my host by in my theme like this page i use wp ajax and because my wp-admin is locked this form not work what should had i to do for this problem? when user submit the form get this alert of protection

http://www.onwebsite.ir is requesting your username and password. The site says: “Admins Area!”

is there any way i do my ajax requests in an other path? or is has way for send information protection with form just for ajax file?

and in the second action how can i change wp-login.php file url?

thank you guys

This is the usual method:

<Files admin-ajax.php>
  Order allow,deny
  Allow from all
  Satisfy any
</Files>

Added to the .htaccess file within wp-admin.