This is a complicated question and cannot be answered by simply looking at the language of deeds and tax map ownership, including the public lands. There may be easements, including "lake rights" to the "landlocked" parcel that arise out of necessity or prior use. You need to take the deeds to a real estate attorney to review, and even then, the use patterns may not be apparent and there may be enforceable adverse possession claims as to some of these easements.
If there is a need to clarify this for some reason and "quiet title" or for someone to enjoin trespass on the easements or, alternatively, to require access to the easements, there may need to be a civil action for declaratory and injunctive relief in Supreme Court (the lowest level of state trial courts of record) brought under the Real Property Law and the Real Property Actions and Proceedings Law.
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Contact a real estate lawyer about adverse possession and easement issues.
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I don't think adverse possession can be claimed against a municipality. Consult a local real estate lawyer.
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Typically adverse possession rights cannot be claimed against a municipality/the government.
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