Custom Fields – How can I remove the publish option for certain users

You can do something like this :

function wpse_113057_hide_publish_buttons(){
 $cpt="your_post_type";// can be post
 global $post;
 if($post->post_type == $cpt && current_user_can('members') ){
  echo '
    <style type="text/css">
      .misc-pub-section, #delete-action {
        display:none;
      }
    </style>
  ';
 }
}
add_action('admin_head-post.php', 'wpse_113057_hide_publish_buttons');
add_action('admin_head-post-new.php', 'wpse_113057_hide_publish_buttons');

I did not find a hook to do this with some PHP.

Hope this helps.