well, the state involved is very relevent but;
typically to make a claim for adverse possession, YOU must file a suit to quiet title and prove why you should be awarded title to the area in question. The courts will make the decision as to the validity of the claim.
you have also left out too many details to even think this is an adverse possession situation. You state there is a right or way. Depending on who owns the ROW property and what is in any involved deed, you may never be able to claim adverse possession of the property.

