Reflected entropy in BCFTs on a black hole background

We obtain the reflected entropy for bipartite mixed state configurations involving two disjoint and adjacent subsystems in two dimensional boundary conformal field theories (BCFT${}_2$s) in a black hole background. The bulk dual is described by an AdS${}_3$ black string geometry truncated by a Karch-Randall brane. The entanglement wedge cross section computed for this geometry matches with the reflected entropy obtained for the BCFT${}_2$ verifying the holographic duality. In this context, we also obtain the analogues of the Page curves for the reflected entropy and investigate the behaviour of the Markov gap.