This may be a small clue to your Ohio connection. I have some sketchy information on a Barnhill who went into Baltimore, MD. It seems the children dispersed from there. One of them may be a link to those mentioned in this forum that is talking about Oldham County, Ky.
It says a son went to Cadiz, Harrison County, Ohio. Cadiz is the seat of government of Harrison County. No given name is mentioned in this information I have on the one that was suppose to have gone to Harrison County, Ohio.
We all grab for straws sometimes hoping for somethingpositive will come up. I hope this bit of information will be of help to you in your research.