She can file the proceeding in Westchester Family Court - so long as he resides in New York, then that state would clearly have jurisdition over him to proceed on the support matter. She may also wish to consider filing for divorce, as she may qualify for spousal support as well as asset distribution (though probably not that much given the short-term duration of the marriage). In any event, have her schedule a phone consultation with a Westchester Child Support attorney.
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She could file a petition in the Family Court county the father is residing in by either going in person, trying to file on line or by hiring an attorney to prepare and file the petition for her. Filing in Family Court is the easiest and quickest way to get support. However, if she is also seeking spousal support (commonly known as "alimony" but called "maintenance" in New York). she may want to file for divorce. A divorce filing must be done in Supreme Court. Your daughter should seek the services of an experienced family and matrimonial law attorney for a consultation prior to doing anything since there are many issues which should be discussed prior to any filing, including, but not limited to, spousal support, child support, custody and parenting time as well as the division of any assets.
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