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Let be a commutative Noetherian ring with non-zero identity, $\fa$ an ideal of , and an --module. In this paper, for fixed integers and a finite $\fa$--torsion --module , we first study the membership of $\Ext^{s+t}_{R}(N, X)$ and $\Ext^{s}_{R}(N, H^{t}_{\fa}(X))$ in Serre subcategories of the category of --modules. Then we present some conditions which ensure the existence of an isomorphism between them. Finally, we introduce the concept of Serre cofiniteness as a generalization of cofiniteness and study this property for certain local cohomology modules.