How do I reflect the wages earned in a different state than the residence? College student earning wages in Ohio but residence is IL. Appears to be taxing in both states?

Review your personal information that you've entered in TurboTax, which is needed to help ensure that you create the correct state tax returns. Also, delete the state returns and start over.  You shouldn't ‌be paying taxes on the same income in both Ohio and IL. 

To delete your OH and IL tax returns, follow the steps below:

1. Launch TurboTax and select State from the menu and Continue
2. On Status of your state returns screen select delete next to OH and IL and confirm.

Refer to the TurboTax article How do I delete my state return in TurboTax Online?

To review your answers in the Personal Info section:

1. Launch TurboTax and select My Info
2. A Personal profile summary screen will pop up
3. Select Edit by your name
4. Scroll through the screens to ensure that you have the correct answers for your state of residence
5. Scroll down to Other State Income and select Edit
6. Check your answer for Did you make money in any other states? Answer Yes, and indicate that you made money in Ohio.

After you complete your federal tax return and you move to the State Taxes sections, both your non-resident Ohio and resident Illinois state returns will be listed.  Prepare your nonresident (OH)  tax return first. You will get a credit on your IL tax return for the taxes that you paid to Ohio.

For additional information, refer to the TurboTax Help articles Do I have to file tax returns in more than one state?,  Why would I have to file a nonresident state return? and How do I file a nonresident state return?

It only appears that way.  Ohio only taxes you on the income you earned there.  Illinois taxes you on all your income, including the income earned in OH. But, then IL gives you a credit, or partial credit for the tax you paid to OH. There is little or no double taxation.

To add to the complexity, Ohio does a convoluted tax calculation for non-residents/part year residents. It calculates tax on total income, then it calculates a non resident/part year resident credit, which it subtracts from the tax it calculated on the total income. The credit is calculated as your non-Ohio income divided by Total adjusted Income multiplied by the total tax. TurboTax (TT)   does this by allocating your income as either Ohio or non-Ohio. W-2 income will be allocated by the state name abbreviation shown in box 15 of your W-2. TT will ask you, item by item, in the state section, how much of your other income is Ohio or non-Ohio income. Make sure that your non-Ohio wages show IL in box 15 of your W-2 screen, with the IL amount in box 16.