In order to work, you will need the library “Category class” : https://wordpress.org/plugins/category-class/
This widget will find the root category which the current post (or category) depends.
Once done, it will display the latest posts from the root category, not for the entire site.
Based on the “Recent post” widget, you will find the same parameters with a new checkbox : you will be able to add the category name in titles.
You can find a demo here : http://www.spoils.fr/
The widget is named “Articles Recents” on the sidebar.