  The potential association between Tidal Disruption Events (TDEs) and
high-energy astrophysical neutrinos implies the acceleration of cosmic rays.
These accelerated particles will initiate electromagnetic (EM) cascades
spanning from keV to GeV energies by the processes related to neutrino
production. We model the EM cascade and neutrino emissions by numerically
solving the time-dependent transport equations and discuss the implications for
AT2019dsg and AT2019fdr in the X-ray and $\gamma$-ray bands. We show that the
$\gamma$-ray constraints from \emph{Fermi} can constrain the size of the
radiation zone and the maximum energy of injected protons, and that the
corresponding expected neutrino event numbers in follow-up searches are limited
to be less than about 0.1. Depending on the efficiency of $p\gamma$
interactions, the X-ray and $\gamma$-ray signals can be expected closer to the
peak of the optical-ultraviolet (OUV) luminosity, or to the time of the
neutrino production.
