  In high energy hadronic collisions, a general CP-violating Higgs boson $\Phi$
with accompanying jets can be efficiently produced via gluon fusion, which is
mediated by heavy quark loops. In this letter we study the dominant sub-channel
$ gg \to \Phi ggg$ of the gluon fusion production process with triple real
emission corrections at order $\alpha_s^5$. We go beyond the heavy top limit
approximation and include the full mass dependence of the top- and bottom-quark
contributions. Furthermore, we show within a toy-model scenario that
bottom-quark loop contributions in combination with large values of $\tan
\beta$ can modify visibly the differential distributions sensitive to
$\mathcal{CP}$-measurements of the Higgs boson particle.
