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Basing on the relativistic theory in superstrong magnetic fields (SMFs), weinvestigate the influence of strong electron screening (SES) on the rates ofnuclear reaction $^{23}$Mg $(p, \gamma)$ $^{24}$Al by three models of Lai (LD),Fushiki et al. (FGP), and Liu et al. (LJ) on the surface of magnetars. Ourresults show that the rates can be greatly enhanced by three orders ofmagnitude due to the influence of SES. The rates in our model are in goodagreement with those of LD and FGP at relatively low density environment (e.g.$\rho_7<0.01$) for $1<B_{12}<10^2$. On the other hand, in relatively highmagnetic fields (e.g. $B_{12}>10^2$), the rates of our model can be 1.58 timesand around three orders of magnitude larger than those of FGP and LD,respectively. The significant increase of the rates of our model for $^{23}$Mg$(p, \gamma)$ $^{24}$Al implies that more $^{23}$Mg will escape from the Ne-Nacycle due to SES in SMFs. As a consequence, the next reaction $^{24}$Al$(\beta^+, \nu)$ $^{24}$Mg will produce more $^{24}$Mg to participate in theMg-Al cycle. Thus, it may lead to synthesize a large amount of production of$A\geq 20$ nuclides (e.g. $^{26}$Al) on the surface of magnetars. These heavyelements (e.g. $^{26}$Al) may be thrown out due to the compact binary mergersof double neutron star (NS-NS) or black hole and neutron star (BH and NS)systems. Our results may help to understand why the $^{26}$Al is alwaysoverabundance in the interstellar space. Our conclusion may be helpful to theinvestigation of the nucleosynthesis of some heavy elements, the energygeneration rate, and the numerical calculations of magnetars evolution.

Resonant nuclear reaction $^{23}$Mg $(p,\gamma)$ $^{24}$Al in strongly screening magnetized neutron star crust