My daughter went to live with her sister in another state.her sister applied for child support do I have to pay

Not enough information.  It is unclear what "applied for child support" means.  If her sister -- presumably, your daughter, and presumably, already emancipated -- applied for welfare benefits, then it is possible that the authorities could eventually attempt to collect any support paid for your child's benefits from the child's parents.  But there are so many missing pieces -- what is the existing custody order/  Where is the other parent?  How old is everyone involved?  What consents were given, by whom, when and why? (etc.) that it is not possible on these facts to be much more specific.  You may want to consult with a family law specialist well versed in such matters.