This is a very sticky situation and it's always been one of my fears. Unfortunately, you probably don't have any proof that you did turn it in, right? So it's just your word against his....
Were you in class the day that you had to turn it in? Maybe you can prove that you were there by showing him your notes or telling him about something he discussed that day?
Do you still have a copy of the paper on your computer? I would print out another copy and give it to him ASAP! Hopefully, he will be willing to work with you.
Good luck!