I inherited 1/3 of my mothers house, my brothers are buying my share as they want to keep the property as rental property. I live in New York State so do I have to pay taxes on my 1/3 when they purchase it.

Maybe, but inherited real property is treated differently. You need to find the value of the property at the time of your mothers death. Divide that by 1/3, your share. If they will pay you that exact value then you do not pay taxes. If they pay you more than the 1/3 value, you will be liable for capital gains. You need to determine if NY has a separate inheritance tax in and above or in addition to any capital gain.

It also depends on whether the estate has been closed and the property has been transferred. So we need more details. When did mom die? Has the estate been closed? Was there more to the estate than the house? Was there a will? Who was executor of the estate?