  We investigate the production of the hidden-charm pentaquark $P_{cs}^0(4459)$
with strangeness in the $K^- p \to J/\psi \Lambda$ reaction, employing two
different theoretical frameworks, i.e., the effective Lagrangian method and the
Regge approach. Having determined all relevant coupling constants, we are able
to compute the total and differential cross sections for the $K^- p \to J/\psi
\Lambda$ reaction. We examine the contributions of $P_{cs}$ with different sets
of spin-parity quantum number assigned. The present results may give a guide
for possible future experiments.
