  We report on evidence for orbital phase-dependence of the gamma-ray emission
from PSR B1957+20 black widow system by using the data of the Fermi Large Area
Telescope. We divide an orbital cycle into two regions: a region containing the
inferior conjunction, and the other region containing rest of the orbital
cycle. We show that the observed spectra for the different orbital regions are
fitted by different functional forms. The spectrum of the orbital region
containing inferior conjunction can be described by a power-law with an
exponential cutoff (PLE) model, which gives the best-fit model for the orbital
phase that does not contain the inferior conjunction, plus an extra component
above ~2.7 GeV. The emission above 3 GeV in this region is detected with a
~7-sigma confidence level. The gamma-ray data above ~2.7 GeV are observed to be
modulated at the orbital period at the ~2.3-sigma level. We anticipate that the
PLE component dominating below ~2.7 GeV originates from the pulsar
magnetosphere. We also show that the inverse-Compton scattering of the thermal
radiation of the companion star off a "cold" ultra-relativistic pulsar wind can
explain the extra component above ~2.7 GeV. The black widow pulsar PSR B1957+20
may be the member of a new class of object, in the sense that the system is
showing gamma-ray emission with both magnetospheric and pulsar wind origins.
