Add a custom category page in WordPress.org

Question

Make a child theme to make your changes to your parent theme
(Zephyr).
Add all your new categories (if you haven’t already). You do that in your site’s admin area, on the Categories page, under Posts. You will see each category has a slug you can modify.
For each of the category pages you want to modify:
- Find the file inside the parent theme folder which your parent theme is using to display categories. This file is called “category.php,” or if that doesn’t exist then it’s “archive.php.” If neither of those exist, then use the file “index.php.” Edit: See Andrii Shekhirev’s more comprehensive answer for specifics about the Zephyr theme, and the ways you can use its archive.php file + associated template file together to build your category page.
- Make a copy of that file, and place it in your child theme folder.
- Rename this file “category-slug.php” replacing “slug” with the slug for your category. You can find this slug listed in the category listing, under posts, in your site’s admin area — it’s the page where you added your new categories. (So if the category is ‘Native Orchids’ and the slug is ‘native-orchids’ then your new file will be named ‘category-native-orchids.php’.)
- Modify this file and/or add css to your child theme’s style.css file to style this page.
- Once you’ve got this working for one category, you can follow the same steps for the other categories.