I have been paying through payroll deductions for medical insurance since January 1, 2015. When I have called the Insurance Company, they have no record of me. I asked my employer for refund - he says no. How can I get my money returned for services not available to me.

Go back as calmly as you can to your employer and demand to see the paper work showing that your premium was paid, and the acknowledgement from the company. You should have received a card, an ID number, and other papers from the insurer. If not, some mistake happened, or your employer hasn't added you to the group policy. That's illegal, and you can tell him that you will report it to the Labor Dept. Ask him in writing in case he fires you.
You leave many unanswered questions. You never got any papers? How many people are in the group policy? (50+ employees must be insured or face a penalty.)

Are you a new hire still on probation?