If you physically work in your home state, for an employer located in another state, generally you only pay state income tax to your home state. But if your employer is located in New York, Pennsylvania, Nebraska, Delaware and Arkansas, the rule is different. NY considers your income to be sourced in NY, so, as others have said, you must file a NY non resident return and pay NY tax. Your employer is, most likely withholding NY tax. Ohio will give you a credit, or partial credit for the tax you pay to NY.
Exception: If you work outside NY as a job requirement (convenience of the employer), you are only subject to New York State income tax on the days you physically work in New York. But if you work outside New York for your own convenience, you are subject to New York State income tax on all your wage income.
Here's a link to New York's memorandum on its "convenience of the employer" tax doctrine regarding non-resident telecommuters: https://www.tax.ny.gov/pdf/memos/income/m06_5i.pdf
