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We demonstrate that the celebrated Stückelberg formalism is <i>modified</i> in the case of a <i>massive</i> four (3 + 1)-dimensional (4D) Abelian 2-form theory due to the presence of a self-duality <i>discrete</i> symmetry in the theory. The <i>latter</i> symmetry entails upon the <i>modified</i> 4D massive Abelian 2-form gauge theory to become a <i>massive</i> model of Hodge theory within the framework of Becchi–Rouet–Stora–Tyutin (BRST) formalism where there is the existence of a set of (anti-)co-BRST transformations corresponding to the <i>usual</i> nilpotent (anti-)BRST transformations. The <i>latter</i> exist in any <i>arbitrary</i> dimension of spacetime for the <i>usual</i> Stückelberg-modified <i>massive</i> Abelian 2-form gauge theory. The modification in the Stückelberg technique is backed by the precise mathematical arguments from the differential geometry where the exterior derivative and Hodge duality operator play the decisive roles. The <i>modified</i> version of the Stückelberg technique remains <i>invariant</i> under the <i>discrete</i> duality transformations which <i>also</i> establish a precise and deep connection between the off-shell nilpotent (anti-)BRST and (anti-)co-BRST transformations. We have clarified a simple trick of using the equations of motion to remove the higher derivative terms in the appropriate Lagrangian densities so that our 4D theory can become consistent.