"During the last 20 years, graphene is driving numerous breakthroughs in optoelectronics. Its derivative, known as graphene nanoribbon (GNR), follows the same path, especially in semiconducting devices. Recently, the cove-shaped GNR (CGNR) was synthesized, showing promising electronic properties. In this work, we uncover the inner mechanisms of charge transport in the CGNR mediated by quasiparticles and extend the analysis for heterojunction conformations. The dynamics of polarons and bipolarons under the influence of an external electric field are simulated through the two-dimensional Su-Schrieffer-Heeger (SSH) model with electron-phonon coupling. We probe polaron's and bipolaron's mobility and effective masses for a wide range of electric field strength regimes. Results reveal that these quasiparticles have distinct transport behaviors due to phonon collision. Regarding the heterojunctions, we report a smooth gap-tuning strategy by adding zig-zag borders at the synthesized CGNR geometry. The proposed transformation also alters the polaron drifting regime, smoothly turning it into a semi-hopping mechanism which suggests a potential tuning strategy to polaron dynamics. The findings contribute to the theoretical understanding of highly confined systems and may inspire future applied investigations in materials science."