At least here in NJ, a road can be a private road or it can be county road - but it cannot be both.
If you have a private road on your property, then you have the right to exclude others from it.
If there is a county road that bisects your property, then you cannot exclude others from using a public roadway.
I am not a NM attorney, laws vary from state to state, therefore you should always consult a local attorney.
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