  We investigate the effect of a magnetic field on cold dense three-flavor
quark matter using an effective model with four-Fermi interactions with
electric and color neutrality taken into account. The gap parameters Delta_1,
Delta_2, and Delta_3 representing respectively the predominant pairing between
down and strange (d-s) quarks, strange and up (s-u) quarks, and up and down
(u-d) quarks, show the de Haas-van Alphen effect, i.e. oscillatory behavior as
a function of the modified magnetic field B that can penetrate the color
superconducting medium. Without applying electric and color neutrality we find
Delta_2 \approx Delta_3 >> Delta_1 for 2 e B / mu_q^2, where e is the modified
electromagnetic coupling constant and mu_q is one third of the baryon chemical
potential. Because the average Fermi surface for each pairing is affected by
taking into account neutrality, the gap structure changes drastically in this
case; we find Delta_1 >> Delta_2 \approx Delta_3 for 2 e B > mu_q^2. We point
out that the magnetic fields as strong as presumably existing inside magnetars
might induce significant deviations from the gap structure Delta_1 \approx
Delta_2 \approx Delta_3 at zero magnetic field.
