We propose extending the minimal scotogenic model with a triplet fermion and a singlet scalar. All the fields change non-trivially under an additional \(Z_{4}\times Z_{2}\) symmetry. The \(Z_{4}\times Z_{2}\) symmetry allows only diagonal Yukawa couplings among different generations of SM leptons and right-handed singlet neutrinos. The one-loop radiative diagrams generate neutrino mass. The Yukawa coupling of the triplet fermion with the inert doublet positively contributes to the muon anomalous magnetic moment.  The imposed \(Z_{4}\times Z_{2}\) symmetry forbids the conventional leptogenesis from the lightest right-handed neutrino decay ( \(N_{1}\) ). The decay of triplet fermion and ( \(N_{2}\) ) can generate a net lepton asymmetry in the muonic sector. Involvement of the Yukawa coupling both in leptogenesis and in the anomalous magnetic moment of the muon results in a strong correlation between leptogenesis and the recent Fermi lab result. We show a viable parameter space for leptogenesis while explaining the Fermi lab results. The inert scalar is the dark matter candidate in this model.