My wife took a job and she and kids moved to OH in Sept rent a place and kids stated school in OH. I lived and worked in KY whole year. We still have house in KY. How can we file tax this year should it be 1. filing jointly 2. filing separately. The issue is with states. I still need to be a resident of KY because I am getting pre-diem from my contract that is required me to travel to OH twice a week. Any suggestion would be great help.

Thanks

If your wife did not have any income during her stay in OH, then you don't file OH tax return. For OH you are nonresident and your wife is part-year resident.
Also even she had some income during her stay in OH, check if it is less than the filing requirement.