  One of the main results of the Fermi Gamma-Ray Space Telescope is the
discovery of {\gamma}-ray selected pulsars. The high magnetic field pulsar, PSR
J0007+7303 in CTA1, was the first ever to be discovered through its
{\gamma}-ray pulsations. Based on analysis of 2 years of LAT survey data, we
report on the discovery of {\gamma}-ray emission in the off-pulse phase
interval at the ~ 6{\sigma} level. The flux from this emission in the energy
range E \geq 100 MeV is F_100 = (1.73\pm0.40)\times10^(-8) photons/cm^2/s and
is best fitted by a power law with a photon index of {\Gamma} = 2.54\pm0.14.
The pulsed {\gamma}-ray flux in the same energy range is F_100 =
(3.95\pm0.07)\times10^(-7) photons/cm^2/s and is best fitted by an
exponentially-cutoff power-law spectrum with a photon index of {\Gamma} = 1.41
\pm 0.23 and a cutoff energy E_c = 4.04 \pm 0.20 GeV. We find no flux
variability neither at the 2009 May glitch nor in the long term behavior. We
model the {\gamma}-ray light curve with two high-altitude emission models, the
outer gap and slot gap, and find that the model that best fits the data depends
strongly on the assumed origin of the off-pulse emission. Both models favor a
large angle between the magnetic axis and observer line of sight, consistent
with the nondetection of radio emission being a geometrical effect. Finally we
discuss how the LAT results bear on the understanding of the cooling of this
neutron star.
