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Yes, being a resident of NY, you will owe taxed in NY State.
Since the employer does not have a presence in NY, he is not required to register in NY and withhold tax on your wages. YOu will have to pay quarterly tax payments to NYS.
You might want to inform your employer to not withhold any taxes in NJ since your services are rendered from NY and not in NJ.
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Please note: This advice is provided with the understanding that all the relevant facts have been provided by you. Any change in facts might affect the advice given and hence may not be relied on in such cases. Nothing contained in this reply was intended or written to be used, can be used by any taxpayer, or may be relied upon or used by any taxpayer for the purposes of avoiding penalties that may be imposed on the taxpayer under the Internal Revenue Code of 1986, as amended.