  We present results on the second-order fluctuations of and correlations among
net baryon number, electric charge and strangeness in (2+1)-flavor lattice QCD
in the presence of a background magnetic field. Simulations are performed using
the tree-level improved gauge action and the highly improved staggered quark
(HISQ) action with a fixed scale approach ($a\simeq$ 0.117 fm). The light quark
mass is set to be 1/10 of the physical strange quark mass and the corresponding
pion mass is about 220 MeV at vanishing magnetic field. Simulations are
performed on $32^3\times N_\tau$ lattices with 9 values of $N_\tau$ varying
from 96 to 6 corresponding to temperatures ranging from zero up to 281 MeV. The
magnetic field strength $eB$ is simulated with 15 different values up to
$\sim$2.5 GeV$^2$ at each nonzero temperature. We find that quadratic
fluctuations and correlations do not show any singular behavior at zero
temperature in the current window of $eB$ while they develop peaked structures
at nonzero temperatures as $eB$ grows. By comparing the electric charge-related
fluctuations and correlations with hadron resonance gas model calculations and
ideal gas limits we find that the changes in degrees of freedom start at lower
temperatures in stronger magnetic fields. Significant effects induced by
magnetic fields on the isospin symmetry and ratios of net baryon number and
baryon-strangeness correlation to strangeness fluctuation are observed, which
could be useful for probing the existence of a magnetic field in heavy-ion
collision experiments.
