4 Answers

Have you asked your neighbour if you can hang things on "HIS" fence? Usually what happens on your side of the fence is your business but I can see his point if he paid for the fence with no contribution from you.Having said that,I don't think there is much he can do about it as long as what you hang there is not detrimental to the structure of the fence.Talk to him.

There are several curious questions that I feel compelled to ask you.

- If the fence was erected on the property line, how did you get away without paying for your half?

-Did he ask you to share the cost and you refused ?

-What kind of fence it it ? Chain link, 12-foot-high-solid-concrete ?

-Would your harmless hanging items be visible or noticeable to your neighbour in any way ?

-Did you ask him about hanging your things? If so, what did he say ?

Why is it on your property? He should have put it up a foot away from the property line. If you paid for the fence, would you want him hanging things that he considered "harmless" on his side of the fence? Think about it. 

As digger has said, if you try to work with your neighbor I am sure that he will make some kind of gesture.  Being that it is on your property, so you say, have you had a survey which would prove that it is on your land?  If it is, he may be more than willing to help you, and himself, and let you hang something harmless to the fence.  Make sure that he sees, and agrees to the hangers, etc..