Can there be in whatever way to disable a choice of adding a brand new publish within Custom Publish Key in WordPress (3.)? I have investigated labels and arguments but aren't able to find something that would resemble this type of feature.

May I request why for you to do this?

I'd in the beginning have recommended altering the abilities for the custom publish type, however i don't believe there's one which limits who are able to add posts, only who are able to edit or publish them.

It looks a bit dirty, but you could attempt unsetting the product within the $submenu global

function hide_add_new_custom_type()
{
    global $submenu;
    // replace my_type with the name of your post type
    unset($submenu['edit.php?post_type=my_type'][10]);
}
add_action('admin_menu', 'hide_add_new_custom_type');

Less than an entire solution. I discovered a little a lot of this problem here on this post.

I desired to disable adding new custom posts for any condition political party website within their 'County' publish types. Since there isn't much possibility of new county lines being attracted in the near future, the 'Add County' feature is much more of the liability than the usual feature.