Custom page only editable by one user

You can enhance the query for backend.
The follow source add the user id to the SQL selct for list posts and remove all posts, there are from other user IDs. List only the posts from the logged in users. But the administrator have full access, he is exclude from this enhancement.

add_filter( 'posts_where', 'fb_add_posts_where' );
function fb_add_posts_where( $where ) {

    if ( ! is_admin() || current_user_can( 'administrator' ) )
        return $where;

    $current_user = wp_get_current_user();
    $where .= ' AND post_author=" . $current_user->ID;

    //var_dump($where);exit;
    return $where;
}

You can enhance this example for much more requirements.