What do recruiters look for to prove employment.

Hey everyone, I recently quit my spring internship 4-months in. Now, the employer is refusing to give me a certificate of completion because I quit before the summer internship portion. If I have a contract signed in March and email exchanges up to my resignation letter, is that enough for proof of employment? Unfortunately, I also never received payment for my internship because in the contract I need to give away what I earned if I quit early. therefore, I can't use payment as proof? What should I do? any advice would be very helpful.