If you want a turned end, short of making a lantern-chuck:
The screw-collet of course should be longer than the lathe collet or chuck-jaws.
For screws finishing longer than the chuck jaws or collet depth, use a simple threaded collet in front of a spindle back-stop that bears on the screw-head.
If the finished screw will be shorter than the lathe collet or chuck, you could use a longer threaded collet whose back end is counter-drilled to clear the head, then tapped for a locking-screw that contacts the screw-head. Use a brass locking-screw, or a steel screw with brass or plastic slug, to avoid damage to the workpiece head.