I feel outdated, last time I went to buy a drill bit at Home Depot, most of the bits were no longer round, as well as the drills.
So I Googled and is this what you are referring to: 
The Phillips/square screw drive, also known as the Quadrex , Pozisquare screw drive, is a combination of the Phillips and Robertson screw drives. While a standard Phillips or Robertson tool can be used, there is also a dedicated tool for it that increases the surface area between the tool and the fastener so it can handle more torque.[52]
Who carries this type screw, I don’t see any at Home Depot, although their deck screws have their own special head, as they come with a special bit.
I have a Hitachi 3.6v cordless driver, guess that won’t have enough power.