  We study a simple extension of the Standard Model supplemented by an
electroweak triplet scalar field to accommodate small neutrino masses by the
type-II seesaw mechanism, while an additional singlet scalar field can play the
role of cold dark matter (DM) in our Universe. This DM candidate is leptophilic
for a wide range of model parameter space, and the lepton flux due to its
annihilation carries information about the neutrino mass hierarchy. Using the
recently released high precision data on positron fraction and flux from the
AMS-02 experiment, we examine the DM interpretation of the observed positron
excess in our model for two kinematically distinct scenarios with the DM and
triplet scalar masses (a) non-degenerate ($m_{\rm DM}\gg m_{\Delta}$), and (b)
quasi-degenerate ($m_{\rm DM} \simeq m_\Delta$). We find that a good fit to the
AMS-02 data can be obtained in both cases (a) and (b) with a normal hierarchy
of neutrino masses, while the inverted hierarchy case is somewhat disfavored.
Although we require a larger boost factor for the normal hierarchy case, this
is still consistent with the current upper limits derived from Fermi-LAT and
IceCube data for case (a). Moreover, the absence of an excess anti-proton flux
as suggested by PAMELA data sets an indirect upper limit on the DM-nucleon
spin-independent elastic scattering cross section which is stronger than the
existing DM direct detection bound from LUX in the AMS-02 preferred DM mass
range.
