Have you received the actual Form 1099-G from the state?  If so, what income is being shown on the form?

If your 1099-G form is for unemployment:

Here's where to report your 1099-G for unemployment or paid family leave.

If you're using the TurboTax mobile app, follow these instructions.

Unemployment compensation and paid family leave are entered in the same place:

1. Open or continue your tax return.
2. Search for 1099-G and select the Jump to link at the top of the search results.
3. On the Did you receive unemployment or paid family leave benefits in 2020? screen, answer Yes.
4. Follow the onscreen instructions to enter your 1099-G information.

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If your 1099-G is for a state refund:

Where do I enter a 1099-G for a state or local tax refund?

https://ttlc.intuit.com/community/entering-importing/help/where-do-i-enter-a-1099-g-for-a-state-or-local-tax-refund/00/25558

I received a fradulant claim that I received unemployment income.  I checked with the state and they said they would send out a corrected form showing I did not receive this income.  Should I leave off of my turbo tax form?

I recommend waiting until you receive the corrected 1099-G form to complete your tax return. 

This will ensure you have the support needed to file an accurate income tax return.  The corrected 1099-G form will be the most accurate information and can be reported as needed on your tax return.