Apply custom category template to subcategories

If a is the category slug, then following code would work –

add_action('template_include', 'wpse129481_template_include');
function wpse129481_template_include($t)
{
    // is category archive page
    if( is_category() )
    {
        // current queried category id from queried object
        $child_id = get_queried_object_id();

        // parent category object, getting it by slug.
        $parent_cat = get_term_by('slug', 'a', 'category');

        // current category object, can also be used get_queried_object()
        $child_cat = get_term($child_id, 'category');

        // important part here is the cat_is_ancestor_of() function.
        // it checks if first category is parent/grand parent of second
        if( isset($parent_cat->term_id) 
            && isset($child_cat->term_id)
            && $parent_cat->term_id != $child_cat->term_id
            && cat_is_ancestor_of( $parent_cat, $child_cat )
        )
        {
            locate_template( array('category-cat-a.php') );
        }
    }
    return $t;
}