According to Gregg Clemmer's book Valor In Gray: The recipients of the Confederate Medal of Honor the Immortal 600 were offered medals around 1900 . The medals were fabricated by the Schwaab Stamp & Seal Co. of Milwaukee. The medals were made of copper alloy and consisted of an ornate horizontal bar with the words...
Two loops from this bar suspended a second smaller horizontal bar with the words...
If the man you are seeking has a card in his CSR from the Confederate Adjutent & Inspector Generals Office with the notice of his Medal of Honor it would not be the Immortal 600 medal. If you tell me this man's name and unit I can look up whether or not he is listed on the Confederate Roll of Honor and thus should have recieved the Confederate Medal of Honor.
For more reading on that I suggest you visit our 7th Mississippi Infantry website (linked below) and scroll down the navigation buttons to the left until you see "Medal of Honor". That will take you to the page for my own 2nd great-grandfather and his A&IGO card. I have posted some information on the page about the history of the CMoH and how to have you ancestor recognized today.