I work in Ohio but live in Indiana. Every year I file my state taxes it says I owe money to both I’m not sure what I’m doing wrong but I know my employer pays state tax

Ohio and Indiana have tax reciprocity with each other.  That means that if you live in one of those states and work in the other, then your W-2 income is taxable only by your resident state.  If your income from Ohio consists only of W-2 income, then you only have to pay tax on it to your home state of Indiana.  If you haven't already done so, you should submit Ohio Form IT-4NR to your employer.  Here's a link to the form:

https://dam.assets.ohio.gov/image/upload/tax.ohio.gov/forms/employer_withholding/generic/wth_it4nr.pdf

Submitting the form will exempt you from Ohio withholding.

"But IN will give you credit for any tax you pay to OH so you are not double taxed." 

Indiana will not grant an "other state credit" for taxes mistakenly withheld for a reciprocal state.  Instead, the taxpayer should seek a refund from the reciprocal state.  See FAQ #7 in this Ohio tax reference:

https://tax.ohio.gov/help-center/faqs/employer-withholding-reciprocity#:~:text=How%20can%20my%20employee%20get,1040%20to%20request%20their%20refund.

Note that reciprocity applies only to wages and salary (W-2) income.

Why is TurboTax making my Indiana resident (employed in Ohio) file an Ohio return when there is no Ohio withholding? Ohio instructions say the following:

A full-year nonresident living in a reciprocal state (Indiana, Kentucky, West Virginia, Michigan or Pennsylvania) does not have to file if the nonresident's only Ohio-sourced income is wages. 

Wages were the only source of Ohio income. I could not delete the Ohio forms.

Thanks

@wmadsen --

How do I delete my state return in TurboTax Online? (intuit.com)

In the Personal Info section, answer No to the question about earning income in another state.

In the personal info section, when it asks if you made money in another state, answer NO, per the reciprocal state instructions, on that page. This will prevent TurboTax from thinking you need to file an OH return.