LordPretender

Based on the native “Recent Posts” widget, this one displays the recent posts accord the root category of the current post (or category).
You will have to define a main and secondary category. 
By default, the main one is used to display the latest posts. If visitors are not currently in the secondary (or sub-categories), then it is this one which is used.
This widget is interresting when you have 2 different categories (with no linked subject) and you want to display the latest posts of the other category, rather than display all (or from the current one).
<h3>Configuration</h3>
The parameters are the same as the native widget, with the addition of :
<ul>
<li>Main category ID ;</li>
<li>Secondary category ID.</li>
</ul>
You will have to enter categories ID (only one per field).

Switch Last Posts Widget

A widget which displays the latest posts according the current category.

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.

Root Category Recent Posts

Another last posts widget which get recent posts only for the current root category.

Switch Last Posts Widget vs Root Category Recent Posts