First gather all of your evidence and meet with a local lawyer who can help you decide if a letter or a lawsuit will be the best option. In reality the small amount of land is rarely worth the aggravation. You do need to be proactive and perhaps the fence should be much closer to the line to eliminate confusion.
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Whose fence is it? Sometimes, neighbors pool money together to put in a fence between their properties. In that case, the fence likely belong to both neighbors.
If the fence is solely yours, your neighbor may not legally attach another object to your fence without your permission. If she does, you can just detach the object.
An element of adverse possession is using the land without the true owner's permission. If you give the neighbor permission to use the fence and your land, there should not be adverse possession. If you give the neighbor permission, that should be written down with you keeping a copy someplace safe for decades.
If you moved in and the fence had already been there, you likely need to search the histories of your land and of the neighbor's land to see whether the prior owners had an agreement about the fence.
There can be future problems if boundary disputes persist, especially if you must disclose this upon any sale. resolving this sooner is always better than later as time is a factor in adverse possession claims. the other attorney is correct in that the expense and aggravation of litigating these disputes can outweigh the value of the strip of land you might be fighting over. If the dispute grows and if attorneys get involved, I know of a Boundary Dispute Mediation Service that might help the parties resolve it more cheaply than court.