I lived in Ohio for 6 months in 2024 and then I lived in Kentucky the last 6 months. Per Turbo tax, I don't report Ohio income, even for the income earned in OH, correct?

Kentucky has reciprocal agreement with Ohio. Under a reciprocal agreement, employees only pay income taxes to their home state (i.e., the state where they live), and are exempt from income taxes in their work state. 

However, if you lived and worked in Ohio the six months then lived and worked in KY, you need to file part-year return for each state. Each state will tax you on income earned while you were living and working in that state. 

How do I file a part-year state return?

Q. Ohio return says that I should show $0 compensation for Ohio, correct?

A. No. 

The reciprocal agreement only applies to full year residents of one of the two states.  This is not the case for you. The Ohio program says that you should show $0 compensation for Ohio,  because it is sensing that you are a full year KY resident.  Go back and change the residency  entry.