XY is a straight wire carrying current I. Every point on XY will form magnetic field lines in the form of concentric circles in a plane perpendicular to the plane of XY. I know that some magnetic field exists at point A with a direction of into the plane of the screen. But no magnetic field lines are there as the concentric magnetic lines end at the point X. How is this possible ?
The wire is only shown to end at X. If it would indeed end there as shown then there would be no current in it in the first place. Currents through wires need a closed loop to flow. So this diagram probably means that the wire is going up and loops around at some far off place. And in that case the magnetic field will be the same as is shown in your XY plane for all corresponding points above and below it.