Undercut screws are often used for fastening door hinges. They feature a flat, undercut, countersunk head with phillips recess. Undercut screws have a flat bottom under the head, as opposed to a conical head that tapers down to the shank. With the conical taper taken out of the equation, the hinge screw sits firmly against the countersunk hole in the hinge, with 100% contact, before the bottom of the head gets anywhere near the surface you are fixing to.

With this, not only is the screw secured, but the hinge plate has no chance of having a space behind it from which to potentially swing or move.