I am a dad living in ny and have a child that was born here but mother lives in LA . in what state will have to look into having joint custody ?

Were or are you married to the mom?  Have you filed any court orders in NY?  In CA, if you are not married and have a child, you need to file a 'paternity action' to establish the dad and address custody, visitation and support.  If the child is a resident of CA then you could file in the appropriate court in LA. There are 2 kinds of custody--legal & physical.  You could possibly share legal custody (decisions regarding health care, education, religion etc.) but you would not share physical custody if you live in NY.  You and the mom could agree on a visitation schedule or the court would make a decision based on what would be in the best interest of the child.