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.
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