In the year of 2014 I was enrolled in NYS Medicaid. Will I need a 1095-A form to file my taxes for the 2015 tax season?
Medicaid does not require a 1095 form. If you had coverage all year, simply mark the corresponding line on your 1040 (line 61 on traditional 1040).
With that said, you may get a Form 1095-B if you had Medicaid, CHIP, or Medicare. This form can help if you or a family member had one of these programs for part of the year and you need to file the 8962 Premium Tax Credit form for other months of the year.
Thus, if you had Medicaid all year, you don't need to worry about your 1095, but if you only had it for part of the year, you may need to reference your 1095-B. If you did not get a 1095-B, try contacting your state medicaid department and following up. They may for example need to resend it.