The correct option is C The electrons keep hitting the fixed positive ions and lose their momentum
The electrons do accelerate under the electric field. But the more they accelerate, the more they collide with positive ions in the metal lattice and lose whatever momentum they gained. In short, if you average out the velocities of all these electrons, they seem to have an average velocity against the direction of the field(since they are negatively charged) which is proportional to the Field applied and this velocity is called the drift velocity.
You can imagine it to be similar to a body falling down through a medium. As it falls faster, the medium’s resistance (what we call drag) increases and at some point they cancel out and the body falls with constant velocity(what we call terminal velocity). This medium resistance and electrical resistance are very similar in many ways.