The number of complex numbers satisfying $\overline{z}=i{z}^2$ is 

$\left|\overline{z}\right|=\left|i{z}^2\right|\Rightarrow \left|z\right|=|z{|}^2$

$\Rightarrow \left|z\right|=0\text{ or }\left|z\right|=1.$

If $\left|z\right|=0,$then $z=0$

If $\left|z\right|=1,$ we get $\overline{z}=1/z$ so that the equation becomes  

$1/z=i{z}^2$

or                                $z^3=-i=i^3\Rightarrow z=i,i\omega ,i{\omega }^2$

where $\omega (\ne 1)$ ) is a cube root of unity