this website has all the forms you will need to file for custody in NYS...
http://www.courts.state.ny.us/courthelp/forms.html
as they say the forms are a bit tricky and you may want to have a lawyer or legal aid help you look over the forms... fyi - in NY the dept of corrections helps out with legal forms they make take over 3 months for you to get an appointment with. So plan ahead.
These are the forms you will need - you may want to check with your county to make sure they have no additional forms or paperwork. Also you will need 3 copies of each to bring to the court house to turn them in.
Support -
http://www.nycourts.gov/forms/familycourt/pdfs/4-3.pdf
This is if BD signed the BC -
http://www.nycourts.gov/forms/familycourt/pdfs/4-18.pdf
This is if BD didn't sign the BC -
http://www.nycourts.gov/forms/familycourt/pdfs/5-1.pdf
This is for Custody -
http://www.nycourts.gov/forms/familycourt/pdfs/gf-17.pdf
This hopefully isn't needed but if it is this is for an order of protection through family court -
http://www.nycourts.gov/forms/familycourt/pdfs/8-2.pdf
All forms use Acrobat reader...