First of all you need to consider what staying in an abusive relationship not only does to you but to your child. Children are sponges and what they see and hear affects them. That being said you should file a petition in family court for custody as well as support. The for,s are available online but also you can get some assistance down at the courthouse. The court clerks however cannot offer you legal advice so you may wish to sit down with an attorney even if for just a consultation. Also if you are fearful of him then you may consider filing for an order of protection.
Please consider all of this and sit down with an attorney as soon as possible. No amount of financial support can help if you are hurt in such a way that you cannot care for your child.
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The above answer does not constitute an attorney client relationship and/ or retention of counsel. This answer is based upon the facts presented and may change if additional information is provided. The rules of the Bar for New York State may require me to advise that this could be construed as attorney advertisement.
You should consult a family lawyer and file a petition in family court.
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You can go to your local family court and file a petition for child support and a petition for family offense, which will get you an Order of Protection against him requiring him to stay away. The child support will give you the necessary financial resources and the Order of Protection the additional safety necessary to leave him.
Are you married? If so, you should consider filing for divorce. If not, then you should definitely consult an attorney as the question becomes how much money you'll need to be able to leave him versus how much income he has (& thus how much supprt he's able to give).
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