Since the current carried by the outer and inner are equal and in opposite direction, magnetic field produced by the cylinders at a point P(distance r from central axis) is

$\Rightarrow {\overrightarrow{B}}_{\mathrm{outer}}=\frac{{\mu }_o}{4\mathrm{\pi }}i\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

$\Rightarrow {\overrightarrow{B}}_{\mathrm{inner}}=-\frac{{\mu }_o}{4\mathrm{\pi }}i\frac{\overrightarrow{dl}\times \overrightarrow{r}}{r^3}$

$\Rightarrow \overrightarrow{B}={\overrightarrow{B}}_{\mathrm{outer}}+{\overrightarrow{B}}_{\mathrm{inner}}=0$