When a current carrying wire is along z-axis, the magnetic field can be found using right hand thumb rule.

Here X represents the field is going in and O represents field is coming out.
First case, if two points in the XY plain are above the wire and at same distance from z-axis, then both will lie in the X region(field going in), thus have same direction of magnetic field and magnitudes of magnetic field would be same.
Second case , if the two points in XY plane are at same distance from z axis but one point is above the wire and one is below it, then the direction of the electric field would be opposite for both the points. One point having X direction (going in) and other having O direction (coming out).
First two cases satisfy options (B),(C) and (D).
Thus, options (B),(C) and (D) are the correct options.