THz radiation by beating two femtosecond laser pulses in magnetized and collisional clustered plasma for different laser profiles is investigated. Laser pulses interaction with clustered plasma gives rise to transverse nonlinear current at beating frequencies and is responsible for THz generation. In this mechanism, cluster plasmon resonance significantly enhances the efficiency and the phase matching amplifies that further. Variation of electric field amplitude on directivity of generated waves is examined analytically, as well as numerically for different laser profiles. The numerical findings indicated that laser pulse profile is an important tool to control plasma dynamics and a technique to devise for THz radiation harness for especial applications. The angular distribution of the radiation pattern of THz radiation in forward direction is obtained and the effect of external magnetic field, frequency of plasma, cluster radius and electron collision frequency on generated THz wave patterns have been considered. The study shows that external magnetic field induced more electron current density leading to an increase in radiation power with no change in directivity diagram. Substantial enhancement in magnitude of the angular distribution of THz radiation in clustered plasma compared with un-clustered plasma was noted.