Based on the relativistic theory of superstrong magnetic field (SMF), by using three models of Lai (LD), Fushiki (FGP), and ours (LJ), we investigate the influence of SMFs due to strong electron screening (SES) on the nuclear reaction 23 Mg (p, γ) 24 Al in magnetars. At relatively low density environment (e.g., ρ 7 < 0.01) and 1 < B 12 < 10 2 , our screening rates are in good agreement with those of LD and FGP. However, in relatively high magnetic fields (e.g., B 12 > 10 2 ), our reaction rates can be 1.58 times and about three orders of magnitude larger than those of FGP and LD, respectively (B 12 , ρ 7 are in units of 10 12 G, 10The significant increase of strongly screening rates can imply that more 23 Mg will escape from the Ne-Na cycle due to SES in a SMF. As a consequence, the next reaction 24 Al (β + , ν) 24 Mg will produce more 24 Mg to participate in the Mg-Al cycle. Thus, it may lead to synthesize a large amount of production of A > 20 nuclides in magnetars, respectively.