Correlation $ \chi^{BQ}_{11} $ and quadratic fluctuations $ \chi^B_2,\ \chi^Q_2,\ \chi^T_2 $ of baryon number $\textit{B}$, electric charge $\textit{Q,}$ and temperature $\textit{T}$ are investigated in a two-flavor Polyakov loop extended Nambu-Jona-Lasinio (PNJL) model at finite temperature and magnetic field. The inverse magnetic catalysis (IMC) effect is introduced through magnetic-field-dependent parameters $ G(eB) $ and $ T_0(eB) $ , and we compare the results in scenarios with and without the IMC effect. Under a nonvanishing magnetic field, correlation $ \chi^{BQ}_{11} $ and fluctuations $ \chi^B_2,\ \chi^Q_2,\ \chi^T_2 $ increase with temperature and then exhibit a peak around the pseudocritical temperatures of chiral restoration and deconfinement phase transitions in the cases with and without the IMC effect. The correlation and fluctuations along the phase transition line under an external magnetic field are characterized by scaled correlation ${\hat {\chi}}_{11}^{BQ}={\chi_{11}^{BQ}(eB,T_{pc}^c(eB))}/{\chi_{11}^{BQ}(eB=0,T_{pc}^c(eB=0))}$ and scaled fluctuations ${\hat {\chi}}_2^{B(Q,T)}={\chi_2^{B(Q,T)}(eB,T_{pc}^c(eB))}/{\chi_2^{B(Q,T)}(eB=0,T_{pc}^c(eB=0))}$ at pseudocritical temperature $ T_{pc}^c $ of chiral restoration phase transition. $ {\hat {\chi}}_{11}^{BQ},\ {\hat {\chi}}_2^{B} $ , and $ {\hat {\chi}}_2^{Q} $ increase with the magnetic field, and the inclusion of the IMC effect enhances their values somewhat. However, $ {\hat {\chi}}_2^{T} $ is altered by the IMC effect. Without the IMC effect, $ {\hat \chi}^T_2 $ increases slightly and then decreases with the magnetic field. Considering the IMC effect using $ G(eB) $ , $ {\hat \chi}^T_2 $ monotonically increases with the magnetic field, and that using $ T_0(eB) $ is a nonmonotonic function of the magnetic field.