http://mafiamembershipcharts.blogspot.com/2016/01/genovese-family-bios-of-early-members.html

You'll have to scroll down to find Scarfo's bio.

This source mention his father Phil Scarfo was a soldier in the Luciano Family who lived in Brooklyn before moving to Jersey in the 1930's as well as a few other notes.

It also acknowledges that in Phil Leonetti's book Phil claims Nick's father Phil was never involved in cosa nostra.