Prevent author role from editing others posts

Using this code snippet makes it that an author will see now only his/her
own posting
and is only able to edit his/her own postings. Only Admins will now be able to edit all posting.

You could try to replace ‘author’ with ‘extension_author’ and see if it works
for you as wished.
(Add snippet in functions.php or your own plugin)

function to_parse_query_useronly( $wp_query ) {
    if ( strpos( $_SERVER[ 'REQUEST_URI' ], '/wp-admin/edit.php' ) !== false ) {
        if ( !current_user_can( 'publish_posts' ) ) {
            global $current_user;
            $wp_query->set( 'author', $current_user->id );
        }
    }
}
add_filter('parse_query', 'to_parse_query_useronly' );