  This paper studies hitting properties for the system of generalized
fractional kinetic equations driven by Gaussian noise fractional in time and
white or colored in space. We derive the mean square modulus of continuity and
some second order properties of the solution. These are applied to deduce lower
and upper bounds for probabilities that the path process hits bounded Borel
sets in terms of the $\mathfrak{g}_q$-capacity and $g_q$-Hausdorff measure,
respectively, which yield the critical dimension for hitting points. Further,
based on some fine analysis of the harmonizable representation for the
solution, we prove that all points are polar in the critical dimension. This
provides strong evidence for the conjecture raised in Hinojosa-Calleja and
Sanz-Sol\'e [Stoch PDE: Anal Comp (2022).
https://doi.org/10.1007/s40072-021-00234-6].
