I don't know if this is possible as i'm far from a coder.
For instance, suppose the ID number of the Category is 6.
It has 2 children or sub categories ID numbered 7 and 8.
If the user clicks on any of these sub categories/ children in a displayed post, then WordPress will look for it's parent ID number 6.
If category-6.php exists, WordPress will load it up instead of category.php.