Talk to a New Jersey property lawyer. Most sidewalks are usually on the public right-or-way and not actually on your property. Checking the property records and surveys can determine that. A lot of homeowners believe they automatically own all land up to the edge of the pavement, and that may or may not be the case.
Most private residential properties include an easement for passage along the edge closest the street. We see evidence of this easement in the form of a sidewalk cutting across the property. The lack of a sidewalk does not necessarily mean there is no such easement. You should check your deed for language pertaining to "easements of record", or for any specifically referenced easements. If nothing in your deed indicates such an easement, then check with the county clerk's office for copies of all recorded easements affecting your property.
The good news is: if no easement exists, you can probably negotiate a reasonable fee from the township in exchange for the easement. I caution against asking too much as then town could easily create the easement by necessity, or take it by eminent domain (to which you would still be entitled to a reasonable fee.)
As to whether you can prevent the construction company from entering onto your property; much depends on whether there exists a recorded easement. I advise against physical confrontation. Call the police to enforce your rights and to protect your property. But as I mentioned above, you first have to know whether the easement exists, and there is a good chance it does.
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