On your category template you can use get_queried_object()
to get the current WP_Term
object. From that you can check the parent
property, which is 0, if it is a parent, or some integer, if it is a child term as it returns the parent term’s ID.
$current_term = get_queried_object();
if ( $current_term->parent ) {
// child term
} else {
// parent term
}