Question

A fixed wire AB carries current I an electron is moving parallel to the wire in which direction does the electron tend to move?

Answer 1

                       I
A ---------------->------------B
      electron------>
By Right hand thumb rule, Magnetic field is downward perpendicular to the plane of paper.
The conventional current direction of electric current is opposite to to motion of electron.
By applying Flemming left hand rule,  the force on electron is away from
wire in the plane of paper.
Therefore the electron will be deflected downward (away from wire) in the plane of paper.

Answer 2

see the diagram.

   A carries the current I.  Then an electron is traveling parallel to the current direction.  We use the Right hand thumb rule with thumb in the direction of the current and curling the fingers in .  The direction of curling of fingers gives us the direction of magnetic field, at the location of the electron charge.

   Now Apply the Fleming's Left hand rule ( F-B-I).  The thumb in the direction force, when forefinger in the direction of B and middle in the direction of current.  

For the left side  electron, the force is towards the wire radially inside.  So the acceleration is perpendicular to the velocity.  So the electron will move in a circle in the horizontal plane.