Belonging to that category posts

Hello.

I’m using more than one category in my wordpress site.
When my visitors choose a category, I want “last 5-10 topics” to be shown in part that named as; “The writings about this topic” in the pages (each category will have its own writings).

I searched about this on google but they are giving informations about
putting it on homepage or on sidebars… But what I want is; for example
I clicked the “people category” and than when I m in the “people page”
I will see writings about “people topic” -not other writings about other topics-on the right side of the page like “widget”.