<p>The main goal of this paper is to construct a proportional analog of the quaternionic fractional Fueter-type operator recently introduced in the literature. We start by establishing a quaternionic version of the well-known proportional fractional integral and derivative with respect to a real-valued function via the Riemann–Liouville fractional derivative. As a main result, we prove a quaternionic proportional fractional Borel–Pompeiu formula based on a quaternionic proportional fractional Stokes formula. These tools allow us to present a Cauchy integral type formula for a quaternionic function theory induced by a quaternionic proportional fractional Fueter-type operator with respect to a real-valued function.</p>