  PKS 1413+135, a compact symmetric object (CSO) with a two-side pc-scale
structure in its miniature radio morphology, is spatially associated with 4FGL
J1416.1+1320 and recently detected with MAGIC telescopes. We comprehensively
analyze its X-ray and GeV gamma-ray observation data for revealing its high
energy radiation physics. It is found that the source is in a low-flux stage
before MJD 58500 and experiences violent outbursts after MJD 58500 in the GeV
band. The flux at 10 GeV varies ~3 orders of magnitude, and the GeV-flux
variation is accompanied by the clear spectral variation, which is
characterized as a soft log-parabola spectrum in the low-flux state and a hard
power-law spectrum in the bright flares. The variability amplitude of X-rays is
lower than that of gamma-rays, and no correlation of variability between
gamma-rays and X-rays is observed. Fitting the broadband spectral energy
distribution during a GeV outburst with a multi-zone leptonic model, we show
that the GeV gamma-rays are attributed to the external Compton process while
the X-rays are hybrid of several components. The predicted TeV gamma-ray flux
during the GeV outburst is consistent with the detection of MAGIC telescopes.
These results, together with its CSO radio morphology, imply that PKS 1413+135
has the episodic nuclear jet activities. The weak gamma-ray emission before MJD
58500 may be from its sub-pc-/pc-scale jet component powered by previous
activities, and the violent outbursts with short-timescale variability after
MJD 58500 could be attributed to the recently restarted jet activity.
