When you say "exactly the same," it must describe something. So "a exactly the same" doesn't make sense. If you are talking about an item, you could say "I like exactly the same thing" or "I want exactly the same thing." Usually, you can just use "same." When you say "exactly the same," you just showmore emphasis.

William is right. Also, a/an/the can only come before a noun or adjective + noun. Exactly is an adverb.