Custom Category Template with getting Posts by Tag

Hi team,

My site has a custom post type with custom taxonomies "category" and "tags".
I would like to set up a custom category page template that shows:

Headline 1
-> all posts of the category with tag "tag1"

Headline 2
-> all posts of the category with tag "tag2"

Headline 3
-> all posts of the category with tag "tag3"

The headlines and the tags will be the same for every category page so they can be hardcoded.

Any directions of how to best achieve this?

Thank you!