You could move this post category to a separate post type.
For this you would need to add a new custom post type, move the posts (for example with the plugin “Post Type Switcher”) and then adjust the theme to load the right posts in the frontend.
With this plugin you can also add new columns to the post admin section in order to sort them in different ways.
https://en-gb.wordpress.org/plugins/codepress-admin-columns/
The exact thing you are after could be done if you create a custom plugin for this, but I don’t think that there’s a plugin for this already as it seems like a feature not many people need.