There are some interesting categories for a given finite Cartan datum, for example, the category \({\mathcal O}\) of certain finitely generated modules of the corresponding semisimple Lie algebra \({\mathfrak g}\), the category of rational modules of the corresponding semisimple, simply connected algebraic group \(G\) over a field of positive characteristic, the category of locally finite modules of the associated quantum algebra \(U\) specialized at an \(l\)-th root of unity. In this paper, the authors investigate a certain semisimple subcategory equipped with a `reduced' tensor product for the three above mentioned situations respectively. Also, they determine the fusion rules for this tensor product in each case via known character formulas for the involved modules.