You posted a new question telling me you live in NY state. I have closed that question because it is a duplicate. You need to keep your responses here in this same question thread.
You will not owe any taxes on this money, regardless of how much you receive. The US does not impose any inheritance taxes. Estate taxes apply in some cases depending on the year the decedent died and the value of his estate, but this only applies to US citizens and does not apply to someone who is not a citizen or resident of this country.
If someone is sending this money here to the US, you need to file Form 3520 with the IRS to report the amount you receive. This is required any time that you receive a gift or inheritance from a foreign source which exceeds $100,000 for the year. There would be no tax due with the filing of this form. It is simply required for informational purposes only.
If the money is not coming to this country but instead being left in a Swiss bank account, then each year that you maintain a foreign bank account which reaches a balance of $10,000 or more during the year, you must report the existence of that account to the IRS by filing form TDF 90-22.1. Again, there is no tax due with this form, but it must be filed annually in any year that you maintain a foreign bank account with a balance of $10,000 or more.
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Thank you fran