  We consider a fermionic dark matter candidate interacting via a scalar
mediator coupled with the Standard Model through a Higgs portal. We consider
general setting including both scalar and pseudoscalar interactions between the
scalar and fermion, and illustrate the relevant features for dark matter
abundance, direct search limits and collider constraints. The case where dark
matter has a self-interaction strength $\left\langle \sigma_V
\right\rangle/m_\psi \sim 0.1-1 \,\mathrm{cm}^2/\mathrm{g}$ is strongly
constrained, in particular by the Big Bang Nucleosynthesis. We show that these
constraints can be alleviated by introducing a new light sterile neutrino $N$.
The allowed region for the extended model consists of a triangle at $10 (\sin
\theta)^{-2/5} \,{\rm MeV} \lesssim m_N \lesssim 1\,{\rm GeV}$.
