  We explore leptogenesis within the E6 inspired U(1) extension of the MSSM in
which exact custodial symmetry forbids tree-level flavour-changing transitions
and the most dangerous baryon and lepton number violating operators. This
supersymmetric (SUSY) model involves extra exotic matter beyond the MSSM. In
the simplest phenomenologically viable scenarios the lightest exotic fermions
are neutral and stable. These states should be substantially lighter than 1 eV
forming hot dark matter in the Universe. The low-energy effective Lagrangian of
the SUSY model under consideration possesses an approximate global U(1)_E
symmetry associated with the exotic states. The U(1)_E symmetry is explicitly
broken because of the interactions between the right-handed neutrino
superfields and exotic matter supermultiplets. As a consequence the decays of
the lightest right-handed neutrino/sneutrino give rise to both U(1)_E and
U(1)_{B-L} asymmetries. When all right-handed neutrino/sneutrino are relatively
light \sim 10^6-10^7 GeV the appropriate amount of the baryon asymmetry can be
induced via these decays if the Yukawa couplings of the lightest right-handed
neutrino superfields to the exotic matter supermultiplets vary between
10^{-4}-10^{-3}.
