This is a question to pose in the Intellectual Property section, as there are specific rules governing intellectual property in international law that fall outside the normal confines of traditional international law rules. I highly recommend hiring (or at least consulting with) an intellectual property attorney with extensive knowledge of international intellectual property laws.
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Personal jurisdiction in internet cases is an issue that courts are still struggling with. This is a complicated and fact-intensive issue, but if the court agrees that there is no personal jurisdiction over you for this case, you can have the case dismissed. Factors that are considered may include how passive or interactive your website is (passive websites are considered to more like advertisements which generally do not confer personal jurisdiction), and whether you made any sales in NY. But you will need to file a motion to dismiss for lack of personal jurisdiction before you answer the complaint, or you may have waived the objection to personal jurisdiction.
You should consult with a NY attorney who is familiar with internet and trademark law. Good luck.
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I would strongly recommend that you seek the assistance of a qualified and experienced trademark attorney licensed in New York, as soon as possible. My colleague is quite correct that the matter of whether the court has jurisdiction over your company is a fairly complex and fact intensive question. More importantly, any direct communication you have with the court could inadvertently subject you to personal jurisdiction in the court. The federal rules specifically require that certain challenges to a court’s jurisdiction be presented in a first response and further state that if they are not presented in a first response, they are deemed waived.
A local, qualified and experienced attorney will be able to guide you depending on your precise factual situation, but it is likely that an attorney would challenge the court's jurisdiction and make a special/limited appearance to challenge the jurisdiction over your company.