How do I create a custom permalink structure for a page template

There are different filters available to create the custom permalinks for the posts, custom posts or pages:

Here is the sample code based on your query:

public function custom_permalink_for_page_template( $url, $post ) {

      if ( is_page() && is_admin() && is_page_template( 'custom_page_template' ) {

         return str_replace( get_site_url(), untrailingslashit( get_site_url() ) . "/custom-permalink-structure", $url );

      } else {
        return $url;
      }
    }

You can also validate the permalink structure settings in the if condition

get_option( 'permalink_structure' )