  In this work we study a class of leptophilic dark matter models, where the
dark matter interacts with the standard model particles via the
$U(1)_{L_i-L_j}$ gauge boson, to explain the $e^{\pm}$ excess in cosmic rays
observed by ATIC and PAMELA experiments, and more recently by Fermi experiment.
There are three types of $U(1)_{L_i-L_j}$ models: a) $U(1)_{L_e - L_\mu}$, b)
$U(1)_{L_e - L_{\tau}}$, and c) $U(1)_ {L_e-L_\tau}$. Although ATIC or Fermi
data is consistent with PAMELA data separately, ATIC and Fermi data do not
agree with each other. We therefore aim to identify which of the three models
can explain which data set better. We find that models a) and b) can give
correct dark matter relic density and explain the ATIC and PAMELA data
simultaneously recur to the Breit-Wigner enhancement. Whereas model c) with a
larger $Z^\prime$ mass can explain Fermi and PAMELA data simultaneously. In all
cases the model parameters are restricted to narrow regions. Future improved
data will decide which set of data are correct and also help to decide the
correct dark matter model.
