W-2 was filed only in Ohio for 2018. Moved to Kentucky in october of 2018. Form 1095-A was filed for both Ohio and Kentucky. How do I handle this situation?

You will have to pay State income tax in both states, proportionate to the time you RESIDED in each. Ohio:  January through September (9 months). and Kentucky, October through December (3 months).   Most states have special forms for partial year residents.

It's gonna be complicated.

The reciprocal state rule is only applicable to full year residents. I assume you worked in KY all year.
You will file a part year resident return for each state. You will pay OH tax on all your income for Jan.-Sep.

You will pay KY tax on all your income Oct-Dec and on your KY wages for Jan.-Sep. KY will give you a credit for the OH tax paid on the Jan-Sep KY wages.

Form 1095-A is irrelevant