The correlations ${\chi }_{11}^{BQ},{\chi }_{11}^{BS},{\chi }_{11}^{QS}$, and quadratic (quartic) fluctuations ${\chi }_{2,4}^B,{\chi }_{2,4}^Q,{\chi }_{2,4}^S$, of baryon number $B$, electric charge $Q$ and strangeness $S$ are investigated in a three-flavor PNJL model at finite temperature and magnetic field. The inverse magnetic catalysis (IMC) effect is introduced through the magnetic field dependent parameters $G(eB)$ or $T_0(eB)$, and we make comparison of the results in the cases with and without IMC effect. Since including IMC effect does not change the strength of phase transition under external magnetic field, it does not lead to qualitative difference in the correlations and fluctuations, but modifies their values. The correlations and fluctuations increase with temperature, and then show the peak around the pseudocritical temperatures of chiral restoration and deconfinement phase transitions. The peak structure in ${\chi }_{11}^{BQ}$, ${\chi }_4^B$, and ${\chi }_4^Q$ are much more apparent than in others. The correlations and fluctuations along the phase transition line under external magnetic field are characterized by the scaled correlations ${\widehat{\chi }}_{11}^{XY}=\frac{{\chi }_{11}^{XY}(eB,T_{pc}^c(eB))}{{\chi }_{11}^{XY}(eB=0,T_{pc}^c(eB=0))}$ and scaled quadratic (quartic) fluctuations ${\widehat{\chi }}_{2,4}^X=\frac{{\chi }_{2,4}^X(eB,T_{pc}^c(eB))}{{\chi }_{2,4}^X(eB=0,T_{pc}^c(eB=0))}$, with $X,Y=B$, $Q$, $S$, and $X\ne Y$ at the pseudocritical temperature $T_{pc}^c$ of chiral restoration phase transition. They increase with magnetic fields due to the increase of phase transition strength under magnetic fields. Among them, ${\widehat{\chi }}_{11}^{BQ}$ increases fastest, which may serve as the magnetometer of QCD.

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• QCD phase transitions
• Quark matter