Before we put our fence up, we asked our neighbor if he would like to share the fence line, including costs and he said yes. When the day came to erect the fence, we called the neighbor and he said he could not afford it at that time and he also wanted to change the location of where the fence came out on the side of the house. We did not want to change the location of the fence and told him we would not change the location and that if he wasn't able to pay then we were going to go ahead with the fence and move it off the property line and onto our property-I believe this was 2 ft. Six months later, while we were out of town, our neighbor attached to our fence without our consent. We have since tried to do the "neighborly" thing and come to some sort of agreement. He has yet to pay for a portion of the fence and has not removed from our fence. My question is this... are verbal agreements binding in the state of Ohio and can we legally remove the fence since it is on our property?

Even though he is right next door you need to send him a certifed letter of notice to remove his attachments and encroachment by a certain date. After that date passes and you have your signed letter receipt you can "detach him." He isn't being neighborly so protect yourself from his future acts.