Archive page by category

I’m working on a site for a client who posts news updates for their members. Their news posts are broken down into 6 categories (currently, but this could change). I’m wondering if there is a way to make an archive type page with sections showing the 3 newest posts in a category, like on some newspaper or magazine websites.

Any help/suggestions would be appreciated!

Please reference the following:

https://wphierarchy.com/
https://developer.wordpress.org/themes/basics/template-hierarchy/