  The late-time evolution of Dirac field around spherically symmetric black
hole surrounded by quintessece is studied numerically. Our results show, for
lower values of the quintessence state parameter \epsilon, Dirac field decays
as power-law tail but with a slower decay rate than the corresponding
Schwarzschild case. But for \epsilon<-1/3, all the \ell-poles of the Dirac
field give up the power-law decay form and relax to a constant residual field
at asymptotically late times. The value of this residual field for which the
field settles down varies on different surfaces. It has the lowest value on the
black hole event horizon, increases as the radial distance increases and
maximizes on the cosmological horizon.
