Render sub-paragraph in parent template
You should be able to render the sub paragraph - without any loop, just like every other field - with

{{ content.field_name }}

If you really need the loop for some special markup you can try something like

{% for key, item in content.field_name if key|first != '#' %}
  &lt;div class="some_additional_markup"&gt;
    {{ item }}
  &lt;/div&gt;
{% endfor %}