ALL your income, including your earnings from PA. is taxable by Ohio. Since the two states have tax reciprocity, your PA W-2 earnings are not taxable by PA.
Since your PA employer mistakenly withheld PA taxes, you must file a non-resident PA tax return in addition to your home state OH return. On the PA return you should show the PA withholding but allocate zero income to PA. This should result in your receiving a full refund of the incorrectly withheld PA taxes.
In future, if you ever take a job in PA, file PA Form REV-419 with your PA employer. This will prevent the incorrect withholding of PA taxes. Here's a link to the form:
https://www.revenue.pa.gov/FormsandPublications/FormsforBusinesses/EmployerWithholding/Documents/rev...
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
