In this paper,we study the influences of magnetic fields on the coexistence of diquark and chiral condensates in an extended Nambu-Jona-Lasinio model with QCD axial anomaly,as it relates to color-flavor-locked quark matter.Due to the coupling of rotated-charged quarks to magnetic fields,diquark condensates become split,and the coexistence region is thus superseded in favor of a specific diquark Bose-Einstein condensation (BEC),denoted as the BECI phase.For strong magnetic fields,we find that the BECI transition is pushed to larger quark chemical potentials.The effect of magnetic catalysis tends to disrupt the BEC-BCS (Bardeen-Cooper-Schrieffer) crossover predicted in previous works.For intermediate fields,the effect of inverse magnetic catalysis is observed,and the axial-anomaly-induced phase structure is essentially unchanged.