My father died and he didn't have a will i'm one of 4 children and he didn't have a spouse what are my rights in NY?

I am sorry for your loss.  I am assuming the following from your question: that there is no surviving spouse.  You would each receive the same portion of the estate  (i.e., in equal shares).  Here is the statute:

§ 4-1.1 Descent and distribution of a decedent's estate
The property of a decedent not disposed of by will shall be distributed as provided in this section. In computing said distribution, debts, administration expenses and reasonable funeral expenses shall be deducted but all estate taxes shall be disregarded, except that nothing contained herein relieves a distributee from contributing to all such taxes the amounts apportioned against him or her under 2-1.8.

Distribution shall then be as follows:

(a) If a decedent is survived by:

(3) Issue and no spouse, the whole to the issue, by representation.