As a non-resident, do I need to pay New York State income tax on visits to New York City for business?

For example, I am a non-resident that works for a company that is not based in New York, but I do occasionally visit New York City for meetings. Can NYS tax the portion of my non-resident income simply because I conducted business in the state for a few hours?

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Orignal From: As a non-resident, do I need to pay New York State income tax on visits to New York City for business?