Add the chopped chicken and drained black beans to a large bowl. Finely dice the red onion. Remove the seeds from the jalapeño, then finely dice. Pull the cilantro leaves from their stems and roughly chop. Add the onion, jalapeño, cilantro, shredded cheddar, chili powder, smoked paprika, salt, and BBQ sauce to the bowl with the chicken and beans. Stir until everything is evenly combined.