  We consider direct detection prospects for a class of simplified models of
fermionic dark matter (DM) coupled to left and right-handed Standard Model
fermions via two charged scalar mediators with arbitrary mixing angle $\alpha$.
DM interactions with the nucleus are mediated by higher electromagnetic
moments, which, for Majorana DM, is the anapole moment. After giving a full
analytic calculation of the anapole moment, including its $\alpha$ dependence,
and matching with limits in the literature, we compute the DM-nucleon
scattering cross-section and show the LUX and future LZ constraints on the
parameter space of these models. We then compare these results with constraints
coming from $Fermi$-LAT continuum and line searches. Results in the
supersymmetric limit of these simplified models are provided in all cases. We
find that future direct detection experiments will be able to probe most of the
parameter space of these models for $\mathcal{O}(100-200)$ GeV DM and lightest
mediator mass $\lesssim \mathcal{O}(5\%)$ larger than the DM mass. The direct
detection prospects dwindle for larger DM mass and larger mass gap between the
DM and the lightest mediator mass, although appreciable regions are still
probed for $\mathcal{O}(200)$ GeV DM and lightest mediator mass $\lesssim
\mathcal{O}(20\%)$ larger than the DM mass. The direct detection bounds are
also attenuated near certain "blind spots" in the parameter space, where the
anapole moment is severely suppressed due to cancellation of different terms.
We carefully study these blind spots and the associated $Fermi$-LAT signals in
these regions.
