Prevent Page/Post From Being Created based on Pages/Posts per User per Time Unit

You will need to interrupt the post submission process much sooner. Your code hooked to admin_init stands a pretty good chance of working, with a modification or two, and wp_die is pretty harsh. I’d just redirect back to the originating page without saving, if it were me.

Something like (untested)…

function check_post_limit() {
  if (!isset($_POST['ID'])) return;

  global $wpdb;

  if( $userdata->ID != 1) {
    $post_count = $wpdb->get_var( "SELECT count(*) FROM $wpdb->posts WHERE   DATE(post_modified) = DATE(NOW()) AND post_author = $userdata->ID" );
  }

  if( isset($post_count) && $post_count > 3 ) {
    wp_safe_redirect(admin_url('post.php?post=".$_POST["post_ID'].'&action=edit'));
    exit;
  }
}

A couple of notes:

  1. Your code as written would have thrown a notice for the user with ID
    == 1 because $post_count would not be set.
  2. Checking for user ID == 1 is questionable. Suppose your admin (which
    is what I assume you want) has some other ID (and for security it is
    probably a good idea to have your admin have some other ID). I’d
    write the check based on user role instead.

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