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<jats:title>ABSTRACT</jats:title> <jats:p>Based on more than seven years of <jats:italic>Fermi</jats:italic> Large Area Telescope Pass 8 data, we report on a detailed analysis of the bright gamma-ray pulsar (PSR) J0007+7303. We confirm that PSR J0007+7303 is significantly detected as a point source also during the off-peak phases with a test statistic value of 262 (∼16<jats:italic>σ</jats:italic>). In the description of the off-peak spectrum of PSR J0007+7303, a power law with an exponential cutoff at 2.7 ± 1.2 ± 1.3 GeV (the first/second uncertainties correspond to statistical/systematic errors) is preferred over a single power law at a level of 3.5<jats:italic>σ</jats:italic>. The possible existence of a cutoff hints at a magnetospheric origin of the emission. In addition, no extended gamma-ray emission is detected that is compatible with either the supernova remnant (CTA 1) or the very high-energy (&gt;100 GeV) pulsar wind nebula. A flux upper limit of 6.5 × 10<jats:sup>−12</jats:sup> erg cm<jats:sup>−2</jats:sup> s<jats:sup>−1</jats:sup> in the energy range 10–300 GeV is reported, for an extended source assuming the morphology of the VERITAS detection. During on-peak phases, a sub-exponential cutoff is significantly preferred (∼11<jats:italic>σ</jats:italic>) for representing the spectral energy distribution, in both the phase-averaged and phase-resolved spectra. Three glitches are detected during the observation period and we found no flux variability at the time of the glitches or in the long-term behavior. We also report the discovery of a previously unknown gamma-ray source in the vicinity of PSR J0007+7303, Fermi J0020+7328, which we associate with the <jats:italic>z</jats:italic> = 1.781 quasar S5 0016+73. A concurrent analysis of this source is needed to correctly characterize the behavior of CTA 1 and it is also presented in the paper.</jats:p>