My neighbor says that the fence that is on the property line ins his, we think it is ours, and have asked his 6 year old child to not climb the fence. He does not feel we have the right to ask his son ...
If the fence is on your property, you obviously have a right to control what happens. Rather than getting technical about who's it is, which would probably lead to an argument, I would at least try explaining to the neighbor that you're just concerned for his sons safety and not so much about being held liable. Since you have already told them not to climb the fence, and even if it is on your property, you are really not liable since you have disclosed that he needs to stay off it.