Indecomposable Representations of the Superalgebra $B(1,2)$

Finite-dimensional indecomposable superbimodules over the superalgebra $B(1,2)$ are treated. We propound a method for constructing indecomposable alternative superbimodules over $B(1,2)$ containing a given socle (such can be presented by any irreducible module over $B(1,2)$). The method is based on adding on the Jordan basis. Also, for the characteristic 3 case, we give examples of Jordan indecomposable superbimodules which are not alternative.