What would be my rights in estate of the house, if stepfather passes?

You should address this situation now before your stepfather passes. You have the best chance of getting anything you're entitled to now. Your standing with regard to the house depends upon the capacity in which your mother and stepfather bought it. If they purchased it as joint tenants, then your stepfather owns 100% of it now. If they held it as tenants in common, then depending upon it's value, you may be entitled to something. Whatever other assets your mother had would also be subject to NY's intestacy laws. You should consult with an Estates attorney sooner rather than later.

Most likely your Mom's portion passed to your step-father and he does not have a will naming you as a beneficiary you probably get nothing.

It really depends on how the house was titled. If the house was titled as tenants in the entirety or as joint tenants, then your step father owns the house, and can do anything he wants with it. If it was titled as tenants in common, then you have rights in 1/2 of the property and can force a sale. A quick trip to the county clerk in Mineola or a call to a title company should resolve this. You probably need an attorney, since your mother likely owned items in her own name, which you may have an interest in.

What you are entitled to, if anything, will depend on how the property is titled. Since spouses usually purchase property as joint tenants, it is likely that the house is now owned entirely by your stepfather. In that case, he is free to do whatever he wants with the house, including leaving it to his children. However, if your mother contributed to the cost of the house and you have a good relationship with your stepfather, he may feel a moral obligation to provide for you in some manner. He could include a bequest to you in his will, or he may be willing to buy out what essentially would have been your mother's interest in the house. If you mother owned any assets in her own name, depending on their value, you may be entitled to some of those assets. I would talk to your stepfather as soon as possible about this matter.