The 1951 "Handbook of American Railroads" by Robert G. Lewis lists the New York Connecting Rail Road Company as a "paper railroad" owning 9 miles of track and holding an additional 11.5 miles of trackage rights on the LIRR to reach Bay Ridge Yard. The nine miles, which includes the famous Hell Gate Bridge and its approaches, is electrified and has always been standard gauge.
New York Connecting was set up in 1914 as a part of the New Haven's Hell Gate Bridge project. It provided a connection between the NH and the PRR. It owned no equipment. The NH (and it's successor, Penn Central,) handled all operations. However, the New York Conecting did report separately to the ICC and had the status of a Class 1 railroad back in 1951.
Freight for the PRR was interchanged by car float at Bay Ridge. NH passenger trains to Penn Station used the NY Connecting reach the PRR at Sunnyside Jct. on Long Island. This is the route now used by Amtrak's New York-Boston trains and by Providence & Worcester stone trains for the New York & Atlantic at Fresh Pond Jct.
I doubt there was ever a narrow gauge component (unless there was some sort of temporary tramway used during the construction of the massive approaches the the bridge.)