  What is conducted in the present work is the study of self-gravity effects on
vertical structure of magnetized neutrino-dominated accretion disc (termed NDAF
and considered as a central engine for Gamma-ray bursts (GRBs)). Some of the
disc physical time scales such as viscous, cooling and diffusion time scales,
that are supposed to play a pivotal role in the late time evolutions of the
disc, have been studied. It is of our interest to investigate the possibility
of the X-ray flares occurrence, observed in late time GRB's extended emission
through the "magnetic barrier" and "fragmentation" processes in our model. The
results lead us to interpret self-gravity as an amplifier for Blandford-Payne
luminosity (BP power) and the generated magnetic field, but a suppressor for
neutrino luminosity and magnetic barrier process via highlighting fragmentation
mechanism in the outer disc, especially for the higher mass accretion rates.
