  The superconducting s-wave state in Weyl semimetals in a strong
strain-induced pseudomagnetic field is investigated in a model with local
four-fermion interaction. It is found that only the inter-node pairing is
possible in the lowest pseudo-Landau level approximation. Unlike the case of
the lowest Landau level in a conventional magnetic field, the corresponding gap
equation has only a trivial solution. Nevertheless, superconductivity can be
induced via the proximity effect with a usual s-wave spin-singlet
superconductor. Since a pseudomagnetic field is present necessarily at the
surface of a Weyl semimetal, the proximity effect is strongly affected by the
pseudomagnetic field. The analysis of such an effect showed that while no gap
is opened in the spectrum, the degeneracy of energy levels is lifted. The
unique character of the proximity effect in Weyl semimetals can be probed via
the density of states, the spectral function, and the tunneling current. The
density of states does not vanish at small energies and scales linearly with
the pseudomagnetic field strength. This scaling is manifested also in the
tunneling current.
