There are two pieces: granting access and restricting access, and two basic ways to achieve the desired access and restrictions:
- Start with user(s) who have too little access and elevate them
- Start with user(s) who have too much access and restrict them
You can also use some combination of the two. Based on the goals you state above, I would do it this way:
- Set UserA to WordPress role of Subsriber
- Assign a Section Role of Post Author to UserA for the desired category (WP Admin > Roles > Section Roles)
If some users need to retain a higher WordPress role but still be limited in posting categories, you will also need to define that extra restriction as follows:
- Go to the Exclusive Section admin page (WP Admin > Roles > Exclusive Sections)
- Scroll to the bottom, then up a bit to the "select for all categories" table
- Check the boxes for "Post Contributor" and "Post Author". Also "Post Editor" if you want to restrict WP editors.
- Scroll back to the top
- Confirm the dropdown next to Update button says "ignored - section / object role required"
- Click Update
- In the future, repeat for any new categories (future versions may enable inherited or default Exclusive roles for new categories)
Now Contributor and Authors (and editors, if you made that role exclusive) will not be able to post in any existing category unless you assign them a Section Role for it, as explained for UserA above.
Having said this, I did a trial run and discovered a few potential glitches. I recommend reading my Release Notes for version 0.9.27 before proceeding.