  This study explores a minimal renormalizable dark matter (DM) model,
incorporating a sub-GeV Majorana DM and a singlet scalar particle $\phi$. Using
scalar and pseudo-scalar interactions (couplings $c_s$ and $c_p$), we
investigate implications for DM detection, considering $s$-wave, $p$-wave, and
combined ($s$+$p$ wave) contributions in DM annihilation cross-section, as well
as loop-correction contributions to DM-nucleon elastic scattering. Identifying
a broad parameter space ($10 \,\rm{MeV} < m_\chi \lesssim m_\phi$) within the
$2\sigma$ allowed region, we explore scenarios ($\left|c_s\right|\gg
\left|c_p\right|$, $\left|c_s\right|\ll \left|c_p\right|$, and
$\left|c_s\right|\approx \left|c_p\right|$). We find that (i) a non-zero
pseudo-scalar coupling alleviates direct detection constraints as a comparison
with the previous pure scalar coupling case; (ii) CMB observations set
stringent limits on pseudo-scalar interaction dominant cases, making $s$-wave
annihilation viable only for $m_\chi>1\,\rm{GeV}$; (iii) the preferred
$\phi$-resonance region can be tested in the future indirect detection
experiments, such as e-ASTROGAM.
