Using the symmetry-preserving vector-vector contact interaction model within the Schwinger-Dyson equation framework, we investigate the QCD phase diagram under the influence of an external magnetic field eB, at finite temperature T and quark chemical potential \(\mu \) . At finite temperature, when the magnetic field effect is not included in the effective coupling of the contact interaction, we observe the magnetic catalysis (MC) effect. However, when we account for the magnetic field eB in the effective coupling, we observe the magnetic inhibition effect, or inverse magnetic catalysis (IMC). At finite temperature T and chemical potential \(\mu \) , we construct the QCD phase diagram in the presence of a magnetic field, considering both cases with and without eB-dependent contact interaction coupling. Our findings indicate that the entire critical line separating the chiral symmetry breaking-confinement phase from the chiral symmetry restoration-deconfinement phase is enhanced without eB-dependent interactions, while it is suppressed with such interactions. Additionally, we identify the effects of the magnetic catalysis (MC) and inverse magnetic catalysis (IMC) on the positioning of the critical endpoint.
