Unless there is another provision in the parent's dissolution settlement, child support ends at the age of majority. In most states, this is 18.
Some states (missouri, for example) require parents to continue to provide some financial assistance for college up to a certain age if that child attends their state's schools. There are caveats to this however, and if NY is one of those states, you need to check the rgulations there. A NY family law attorney would be able to tell you, as would your local Family Law Assistance Center. Good luck !
If the state in question is New York, the child support, and in appropriate circumstances payment for college expenses, ends at the age of 21. However, the underlying child support obligation may be modified if the child is attending college away from home to reduce duplication of certain types of expenses. In addition, New York courts have held that depending on the language of the separation agreement, parent's obligation to pay for college may extend past the age of 21. I would suggest that you discuss these issues with an attorney practicing family law in New York.
One little detail of your question which needs to be addressed is the idea that the child is getting the support. Technically, under most circumstances, the custodial parent (not the child) will receive the support from the non-custodial parent. Child support in New York is payable until the child reaches age 21, unless the child is sooner emancipated. A child attending college would usually not be deemed emancipated, unless, for example, the child works full-time while attending college and is not being supported by, or residing with, either parent. A child support obligation may be reduced for a child living away from home while attending college if the non-custodial parent is paying a portion of the child's room and board expenses while at college.