The answer is yes to both. You need to file a non-resident NY return to reconcile the NY sourced income there. Do that return first and take note of the actual taxes paid on the UI. You will use those numbers to then claim a credit on your OH return for taxes paid to another state.
First be sure, you have indicated on in the "My Info" section that you have income from another state (NY). This will generate the nonresident return for NY.
Then "Continue" your OH return and you will arrive at the " OH credits and taxes" page. In the "Personal, home and family credits" section you will find the credit for taxes paid to other states.
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