  It has been recently pointed out that a momentum-dependent coupling of the
asymmetric Dark Matter (ADM) with nucleons can explain the broad disagreement
between helioseismological observables and the predictions of standard solar
models. In this paper, we propose a minimal simplified ADM model consisting of
a scalar and a pseudoscalar mediator, in addition to a Dirac fermionic DM, for
generating such momentum-dependent interactions. Remarkably, the pseudoscalar
with mass around 750 GeV can simultaneously explain the solar anomaly and the
recent diphoton excess observed by both ATLAS and CMS experiments in the early
$\sqrt s=13$ TeV LHC data. In this framework, the total width of the resonance
is naturally large, as suggested by the ATLAS experiment, since the resonance
mostly decays to the ADM pair. The model predicts the existence of a new light
scalar in the GeV range, interacting with quarks, and observable dijet, monojet
and $t\bar{t}$ signatures for the 750 GeV resonance at the LHC.
