What happens if someone uses a special attack on a counter?

Question

What happens if I use Counter and someone uses a Special Attack on me?

Answer 1

Counter can reflect the following special moves:

1. Hidden Power in Generations II and III, regardless of actual type
2. Beat Up in Generations II and III

If Counter is used on any other special move, it will fail.

Counter (Bulbapedia)

Answer 2

Their attack will go through without anything happening and counter will be wasted. The same will happen if mirror coat is used for a physical attack.