It is hard to tell your mathematical background from the question, so maybe an explanation for a more simple, but similar, problem will help.
Let’s say you have a 1 DOF robot, and command it with 2 DOF tasks. It has a link length of 1, so it can move along a unit circle about the origin of a coordinate system. If you command it to go to position (1, 0), it will do so. Same thing if you command (0, 1), or (0.707, 0.707). But if you tell the robot to go to (1, 1), or (0.2, 0.5), or any of a double infinity of other points, it cannot achieve that pose. It will not perform “jerky motion”; instead, the math will not be solvable.
Mathematically, the inverse kinematics are unsolvable. For the situation you describe, you are trying to solve six independent equations using only four variables.