  Solar photospheric magnetic field plays a dominant role in the variability of
total solar irradiance (TSI). The modulation of magnetic flux at six specific
ranges on TSI is characterized for the first time. The daily flux values of
magnetic field at four ranges are extracted from MDI/{\sl SOHO}, together with
daily flux of active regions (MF$_{\text{ar}}$) and quiet regions
(MF$_{\text{qr}}$); the first four ranges (MF$_{1-4}$) are: 1.5--2.9,
2.9--32.0, 32.0--42.7, and 42.7--380.1 ($\times 10^{18}$ Mx per element),
respectively. Cross-correlograms show that MF$_4$, MF$_{\text{qr}}$, and
MF$_{\text{ar}}$ are positively correlated with TSI, while MF$_2$ is negatively
correlated with TSI; the correlations between MF$_1$, MF$_3$ and TSI are
insignificant. The bootstrapping tests confirm that the impact of MF$_4$ on TSI
is more significant than that of MF$_{\text{ar}}$ and MF$_{\text{qr}}$, and
MF$_{\text{ar}}$ leads TSI by one rotational period. By extracting the
rotational variations in the MFs and TSI, the modulations of the former on the
latter at the solar rotational timescale are clearly illustrated and compared
during solar maximum and minimum times, respectively. Comparison of the
relative amplitudes of the long-term variation show that TSI is in good
agreement with the variation of MF$_4$ and MF$_{\text{ar}}$; besides, MF$_2$ is
in antiphase with TSI, and it lags the latter by about 1.5 years.
