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The impact of severe plastic deformation by high-pressure torsion on the relaxation of the glassy and supercooled liquid states of Pd₄₀Ni₄₀P₂₀ was investigated using a combination of differential scanning calorimetry, low-temperature heat capacity, and fluctuation electron microscopy. The changes in the calorimetric signals due to deformation and subsequent heat treatments were analyzed and a correlation between deformation (rejuvenation) and annealing (relaxation) was found in relation to medium-range order (MRO). Moreover, a coupling between the occurrence of an exothermic peak in the supercooled liquid state and specific changes in the MRO types were identified. These findings are comprehended in a potential energy landscape scheme offering a new approach for MRO engineering of glasses.