Category-sensitive archive page

I am trying to create a category archive page, in which links to posts (not an excerpt of the post) from a category is displayed, sorted by date. I understand that this can be done by creating a custom archive page using page template but…

How do I pass the category id of the category I want over to the custom page template? Say in a theme I have a link for my category.php which says “View Archive for this Category” – I could retrieve the cat-id, but how do I pass it over to the custom page?

(Compounding the problem, I am using permalink so my URL are like: https://www.gamestopica.net/about/ — can I just inject query string at the end?)