The company I currently work for expects a minimum of two years of service in the organisation, although there is no clause in the contract that enforces this.
Working for this company is now causing issues for my health and I have decided to leave the company, however my employer refuses to provide a relieving letter as this two years minimum was not met.
How can I explain to future potential employers why I am unable to provide a reference / relieving letter from this company?
I don't know about your country. I'm from Indonesia so it's probably not much different. In my country, if you're a fresh graduate with 2 years of experience, they rarely ask for references. Sure, references will boost your chances of getting hired but they are not always necessary.
My suggestion is just send out your resume or CV. If they ask you for references, you may give your coworker/manager phone number hoping that they explain your problem and that give you a good reference.
I would suggest you to talk with your present HR management. Take advice from them regarding it. If they are unable to solve your issue, then take help of workers union. My father-in-law resides at Bangalore, India, there company do have a employee union. I hope this would help you.
