We extend our approach of modeling spectral energy distribution ( SED ) and lightcurves of blazars to include external Compton ( EC ) emission due to inverse Compton scattering of an external anisotropic target radiation field . We describe the time-dependent impact of such seed photon fields on the evolution of multifrequency emission and spectral variability of blazars using a multi-zone time-dependent leptonic jet model , with radiation feedback , in the internal shock model scenario . We calculate accurate EC-scattered high-energy spectra produced by relativistic electrons throughout the Thomson and Klein-Nishina regimes . We explore the effects of varying the contribution of ( 1 ) a thermal Shakura-Sunyaev accretion disk , ( 2 ) a spherically symmetric shell of broad-line clouds , the broad line region ( BLR ) , and ( 3 ) a hot infrared emitting dusty torus ( DT ) , on the resultant seed photon fields . We let the system evolve to beyond the BLR and within the DT and study the manifestation of the varying target photon fields on the simulated SED and lightcurves of a typical blazar . The calculations of broadband spectra include effects of \gamma - \gamma absorption as \gamma -rays propagate through the photon pool present inside the jet due to synchrotron and inverse Compton processes , but neglect \gamma - \gamma absorption by the BLR and DT photon fields outside the jet . Thus , our account of \gamma - \gamma absorption is a lower limit to this effect . Here , we focus on studying the impact of parameters relevant for EC processes on high-energy ( HE ) emission of blazars .