As a general rule, a neighbor has the right to cut limbs off of trees that overhand from your yard onto the neighbor's yard. However, the neighbor may not enter onto your property (trespass) to limb the tree.
If you dispute the property line, you may have to have the property surveyed and the property line marked. You can then have the fence moved so that it sits on the property line.
I am not sure what you mean by your "vinyl sidings".
This answer is for general education purposes only. It neither creates an attorney-client relationship nor provides legal guidance or advice. The answer is based on the limited information provided and the answer might be different had additional information been provided. You should consult an attorney.