<p>We investigate steady Poisson–Nernst–Planck (PNP) electrodiffusion in a quasi-one-dimensional channel with piecewise-constant permanent charge. Using geometric singular perturbation theory and a governing-system reduction, we prove that the associated boundary-value problem is organized by a nondegenerate saddle–node (fold) bifurcation. In particular, for every nonzero ionic current there exist exactly two steady solutions, while at the reversal potential (zero current) the steady state is unique. On the computational side, we compute the nontrivial steady branch from the reduced governing equation and construct a lightweight surrogate that maps channel parameters and voltage to this branch, allowing rapid and explicit exploration of the solution manifold. The combined analytical and computational framework clarifies how channel geometry, permanent charge, and boundary conditions shape the nonlinear bifurcation structure of steady electrodiffusion, and provides a practical reduced description for scanning and comparing operating regimes.</p>