How do I insert a special entry into a sections list?
There's a special loop variable available in for loops which provides info about the iteration.
In your case you'd just insert that list item after the 2nd iteration:

{% for entry in entriesOnPage %}
    &lt;li class="class-A"&gt;{{ entry.title }}&lt;/li&gt;

    {% if loop.index == 2 %}
        &lt;li class="class-B"&gt;I'm am different&lt;/li&gt;
    {% endif %}
{% endfor %}


If you want to do this only on select pagination pages, you'd additionally compare  against the paginate variable available in between paginate tags:

{% if loop.index == 2 and paginate.currentPage == 12 %}