Paginate based on items in a Category
You're not far away by combining what you already have with the example in the docs! You just need to pass in the category (.relatedTo(category)) and number of entries (.limit(10)) to show on each page.
{% set query = craft.entries()
    .section('mySection')
    .relatedTo(category)
    .limit(10)
%}

{% paginate query as pageInfo, pageEntries %}

{% for entry in pageEntries %}
     &lt;p&gt;&lt;a href=&quot;{{ entry.url }}&quot;&gt;{{entry.title}}&lt;/a&gt;&lt;/p&gt;
{% endfor %}

{% if pageInfo.prevUrl %}&lt;a href=&quot;{{ pageInfo.prevUrl }}&quot;&gt;Previous Page&lt;/a&gt;{% endif %}
{% if pageInfo.nextUrl %}&lt;a href=&quot;{{ pageInfo.nextUrl }}&quot;&gt;Next Page&lt;/a&gt;{% endif %}