If the direction of current in the conductor and the magnetic field are the same, in which way will the conductor move?
It will not move.
The direction of the force on a conductor placed in a magnetic field is given by Fleming's left-hand rule. According to this rule, holding the forefinger, middle finger, and thumb of the left hand in mutually perpendicular directions, the forefinger indicates the direction of the magnetic field and the middle finger, the direction of the current, then the thumb will indicate the direction of the force which results in the motion of the conductor. However, this force is not experienced when the current flows in the direction of the magnetic field. Here, the direction of the current in the conductor and the magnetic field are the same, so, the conductor will not experience any force. Hence, it will not move in any direction.