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We have extensively studied the behavior of pronounced subgap structures on the quasiparticle branches of the current-voltage (I-V) characteristics of intrinsic Josephson junctions (IJJs) in (Bi1-xPbx)2Sr2CaCu2Oy (x=0.15, 0.2) single crystals for their applications in THz range. Six subgap structures are successfully observed between 6.3 and 26.2 mV on the first quasiparticle branch at 4.2 K. The intensities of two typical subgap structures at 6.3 and 8.2 mV are found to be approximately proportional to Ic 2 (critica current)2 over a wide range of temperature between 4.2 and ~ 80 K. They are interpreted with regard to the interference of Raman-active optical phonons with ac Josephson currents in IJJs. Under magnetic field up to 2.5 T they have been affected somewhat in the respect to return current, though the vortex flow also has been induced in IJJs. By microwave application of 2-100 GHz they have been strongly affected so that their peak intensities decrease and then each peak splits into two, with increasing microwave power.