Recently, influence of strong fields on nuclear decay processes is progressively becoming a topic of great interest plus the existence of some ambiguities. In this study, an approximate calculation of the Schrödinger equation with reduced r dependence is employed instead of the classical Coulomb wave function program to provide a description of decay width and decay energy in quasi-static (adiabatic) laser fields. More importantly, going beyond the quasi-static approximation, the strict time evolution of the wave function and the periodic modulation of the decay energy are investigated by solving the time-dependent Schrödinger equation with the split operator method, which captures the dynamical behavior of the $\alpha$ cluster during the decay process. Firstly, our results corroborate earlier reports that the decay width is modified only negligibly by strong laser fields. Likewise, the shift in decay energy is found to be extremely small, which validates the rationality of using fixed experimental decay energies in earlier studies. This modification effect will exist more obviously in nucleus with the higher proton-neutron asymmetry, the lower decay energy and the octupole deformation. Secondly, our results demonstrate that strong fields can indeed produce a periodic modulation of decay energy, with a cycle mean shift on the order of ${10}^{-7}eV$ at an intensity of ${10}^{24}W/c{m}^2$.