Your parents might be able to claim your child on their taxes depending on whether they provide more than half of your child's support and whether the child lives in their house for more than half of the year. There may be some other details that need to be worked out, but those are the two big issues. If you will also be living with your parents then they may be able to claim you as a dependent as well.
The bottom line is this: there are a lot of other facts that can affect whether your parents can claim your child or not, so they would be very, very well-advised to consult with a competent local tax professional, such as an accountant with experience in these sorts of situations, before they do anything on their tax returns. You, and they, should definitely not just rely on answers you get for free online from people whom you've never met and whom you haven't hired to represent you. In other words, please don't take candy from strangers.
My answer does not constitute legal advice and may not be relied upon by anyone for any purpose and does not constitute an attorney/client relationship or an offer to form such a relationship. This disclaimer is intended to be fully compliant with the requirements of Treasury Department Circular 230 and the terms thereof are fully incorporated by reference. If you wish to consult with me please contact me at dana@nytaxcounsel or visit my website at www.nytaxcounsel.comAsk a similar question