How do you page through child entries in a structure?
getPrev, getNext, getPrevSibling, getNextSibling all specify an entry relative to the current one. prevChild and nextChild if they existed would somehow specify an entry relative to a child of the current entry. They don't exist.

What you can do is paginate through the children. Here I use .limit(1) to page through them one at a time, but you could fetch more.

{% set prePaginatedEntries = entry.getChildren().limit(1) %}
{% paginate prePaginatedEntries as entries %}
  {% for oneChild in entries %}
    {# do whatever with oneChild #}
  {% endfor %}
  {# pagination links #}
  {% if paginate.prevUrl %}
    &lt;a href="{{ paginate.prevUrl }}"&gt;Previous Page&lt;/a&gt;
  {% endif %}

  {% if paginate.nextUrl %}
    &lt;a href="{{ paginate.nextUrl }}"&gt;Next Page&lt;/a&gt;
  {% endif %}
{% endpaginate %}