If you are a resident of a state, but also have income from another state you file two tax returns.
If you are a non-resident of OH, you file a Non-resident Tax Return and pay OH income tax on the income you earn in OH.
On your resident state tax return, you are taxed on your worldwide income. You get a credit on your NY Resident tax return for taxes paid to another state so you are not taxed twice on the same income.
It's important that you prepare your Non-resident tax return first, so the credit flows to your Resident tax return.
If the credit is not flowing properly, delete both state returns and start that part of your filing over again.