In collisionless plasmas, turbulence is thought to play an important role in mass transport and energy dissipation. Magnetic fluctuations in the Jovian magnetosphere are essential in a turbulent state. Previous studies of that turbulence have focused on the large scales using low time resolution of magnetic field data. Here we extend those studies to cover a wider range of scales by combining both low and high-time-resolution data of Galileo magnetometer. We use particle data from the plasma instrument and include energetic particle contributions to estimate the local plasma parameters. We obtain 11 power spectra of magnetic field in the frequency range of 10(-4)-1Hz, which covers both magnetohydrodynamics and ion kinetic scales. The frequencies of the evidenced spectral breaks are found to be relatively well correlated with the characteristic scales of heavy ion. The spectral indices below and above the spectral breaks are found to be broad and cover the ranges of 0.6-1.9 and 1.7-2.5, respectively. An analysis of higher-order statistics shows an intermittent feature of the turbulence, found to be more prominent in the plasma sheet than in the lobe. Furthermore, a statistical survey of the power of the fluctuations using low-time-resolution data suggests a radially varying dawn-dusk asymmetry: the total power is larger in the duskside (dawnside) at \textless50 R-J (\textgreater80 R-J), which would reflect flow shear and global magnetospheric activity.