How to add notification in the sidebar of the administration panel when a Custom post type is created? [duplicate]

It is shockingly simple: you have to dyamically set the admin page title, adding a specific markup:

<span class="awaiting-mod count-3">
  <span class="pending-count">3</span>
</span>

So for example if you want to show the number of custom posts you have to do something like this when declaring the options page:

$notif_count = wp_count_posts('my_post_type'); //insert your post type
add_menu_page("My Page Title", 
              "My Page Title <span class="awaiting-mod count-$notif_count"><span class="pending-count">$notif_count</span></span>", 
              'administrator',
              'my_slug', 
              'my_handler_function'
);

Notice the php variable $notif_count inside the second parameter of add_menu_page.