My daughter will be turning 18 years old in one week and she dropped out of school and is moving out to another state leaving her home where her mother has custody of her. Will I still have to pay child support to her mother if my daughter doesn't live there any longer.

In NY support extends to age 21. However, if the child is emancipated (meaning living on their own), then you should not have to pay support. But to terminate support you will have to go back to court and petition for a termination of the support order. Until the order is changed you will have to continue to pay. However, you can include, as part of the petition, that any overages paid after your daughter becomes emancipated are refunded to you.