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Abstract The cooling strength of the Urca pair,⁶³Fe–⁶³Mn, exhibits an extensive range of variation due to the uncertainty in the spin parity of the ground state of⁶³Fe. To investigate the cooling effect of this Urca pair on the thermal evolution of neutron star crusts, we performed simulations on neutron star structure and evolution under various spin-parity assignment scenarios. When adopting recently evaluated nuclear data,⁶³Fe–⁶³Mn emerges as one of the strongest Urca pairs. In the case of MAXI J0556-332,⁶³Fe–⁶³Mn is the only pair above the shallow heating layer, significantly impacting the cooling curve and the superburst ignition. Moreover, the constraint on the past nucleosynthesis reduced to one-quarter of its original value, falling within three decades, which enables the validation of nuclear reaction theories in the outer layers of neutron stars. Our results highlight the need for more precise measurements of theβ⁻decay of⁶³Mn to better determine the Urca cooling effect of the⁶³Fe–⁶³Mn pair in accreted neutron star crusts.