  The degeneracy of the lowest weight representations of the quantum
superalgebra $osp_q(1|2)$ and their tensor products at exceptional values of
%when deformation parameter $q$ takes exceptional values is studied. The main
features of the structures of the finite dimensional lowest weight
representations and their fusion rules are illustrated using realization of
group generators as finite-difference operators acting in the space of the
polynomials. The complete fusion rules for the decompositions of the tensor
products at roots of unity are presented. The appearance of indecomposable
representations in the fusions is described using Clebsh-Gordan coefficients
derived for general values of $q$ and at roots of unity.
