In a recent paper (Luo H et al., 2022), we found that the peak amplitudes of diurnal magnetic variations, measured during martian days (sols) at the InSight landing site, exhibited quasi Carrington-Rotation (qCR) periods at higher eigenmodes of the natural orthogonal components (NOC); these results were based on ~664 sols of magnetic field measurements. However, the source of these periodic variations is still unknown. In this paper we introduce the neutral-wind driven ionospheric dynamo current model (e.g., Lillis et al., 2019) to investigate the source. Four candidates — the draped IMF, electron density/plasma density, the neutral densities, and the electron temperature in the ionosphere with artificial qCR periodicity, are applied in the modeling to find the main factor likely to be causing the observed surface magnetic field variations that exhibit the same qCR periods. Results show that the electron density/plasma density, which controls the total conductivity in the dynamo region, appears to account for the greatest part of the surface qCR variations; its contribution reaches about 67.6%. The draped IMF, the neutral densities, and the electron temperature account, respectively, for only about 12.9%, 10.3%, and 9.2% of the variations. Our study implies that the qCR magnetic variations on the Martian surface are due primarily to variations of the dynamo currents caused by the electron density variations. We suggest also that the time-varying fields with the qCR period could be used to probe the Martian interior's electrical conductivity structure to a depth of at least 700 km.