So you have that $\vec{B} = \frac{a}{r^2}\begin{bmatrix}0 & z & -y\end{bmatrix}$ thus the magnitude is $B = \frac{a}{r^2}\sqrt{z^2+(-y)^2},$ where $a$ is unknown.

Can you write that as a function of $r?$

Can you investigate what happens as $r$ goes to zero?

What magnetic field do you expect at the origin?

What is its magnitude?

Remember that $a$ is an unknown constant. Is there any choice of $a$ that allows $B$ to approach the magnitude it needs as you approach the origin?

Is it the only choice? Is it what you wanted?