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?
Are magnetic fields continuous in empty space (a vacuum)?
If so, try the next five:
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?
If not, can you compute the line integral of the magnetic field in a circle about the origin and compare that to some thing?