The Millside Line was owned by both the Pennsylvania Railroad and the Reading Railroad. The Reading used it as a freight corridor to get cars from Pigeon Car Float (on the Delaware River between Deepwater Point and Wilmington, see below) to the heart of Wilmington. It also connected to The New Castle Industrial Cutoff. It then went to the B&O's Wilmington station. After the station was abandoned it served the Pussey & Jones Shipyard.
When the ship yard operations ceased, the Pennsylvania RR bought the whole line and used it up until the Penn Central era, and then abandoned it. Only some sections of the line are used today.
Pigeon Car Float: The Pigeon Car Float was built by the Reading Railroad in the late 1940s as a rapid way to get oil to Wilmington, DE. The DuPont Company signed a lease to supply a ferry and a line to get from NJ (at Deepwater) over to the Delaware side of Delaware River. The exact abandonment date of the line is not known, but it is believed to have been abandoned in the early 1970s.
Thanks to Christian B. for contributing information about this route.