We study the representation theory of the subregular -algebra of type B and the principal -superalgebra , which are related by an orthosymplectic analogue of Feigin–Semikhatov duality in type A. We establish a block-wise equivalence of weight modules over the -superalgebras by using the relative semi-infinite cohomology functor and spectral flow twists, which generalizes the result of Feigin–Semikhatov–Tipunin for the superconformal algebra. In particular, the correspondence of Wakimoto type free field representations is obtained. When the level of the subregular -algebra is exceptional, we classify the simple modules over the simple quotients and and derive the character formulae.
