Magnetic field d B to a current element at any point on its axis is _____

From the Biot-Savart's law, Magnetic field due to current element

$dB=\frac{{\mu }_{o}idl\sin \left(\theta \right)}{4\pi r^2}$

The magnetic field on a current element is directly proportional to the sine of the angle between the current element and the position vector.

The angle for a point on axis $\theta =0$

so $dB=0$