  The color neutral two-flavor superconducting (2SC) phase of cold and dense
quark matter is studied in the presence of constant magnetic fields and at
moderate baryon densities. In the first part of the paper, a two-flavor
effective Nambu--Jona-Lasinio model consisting of a chiral symmetry breaking
mass gap sigma_{B}, a color superconducting mass gap Delta_{B} and a color
neutrality coefficient mu_{8} is introduced in the presence of a rotated U(1)
magnetic field B. To study the phenomenon of magnetic catalysis in the presence
of strong magnetic fields, the gap equations corresponding to sigma_{B} and
Delta_{B}, as well as mu_{8} are solved in the lowest Landau level
approximation. In the second part of the paper, a detailed numerical analysis
is performed to explore the effect of any arbitrary magnetic field on the above
mass gaps and the color neutrality coefficient. The structure of the chiral
symmetry breaking and color superconducting phases is also presented in the
mu_{c}-B plane, and the effect of the color neutrality coefficient mu_{8} on
the phase structure of the model is explored. As it turns out, whereas the
transition from the chiral symmetry breaking to color superconducting phase is
of first order, nonvanishing mu_{8} affects essentially the second order phase
transition from color superconducting to the normal phase.
