In this paper, we introduce two coupling models of early dark energy (EDE) and cold dark matter aimed at alleviating cosmological tensions. We utilize the EDE component in the coupling models to relieve the Hubble tension, while leveraging the interaction between dark matter and dark energy to alleviate the large-scale structure tension. The interaction is implemented in the form of pure momentum coupling and Yukawa coupling. We employed various cosmological datasets, including cosmic microwave background radiation, baryon acoustic oscillations, Type Ia supernovae, the local distance-ladder data (SH0ES), and the Dark Energy Survey Year-3 data, to analyze our models. We first exclude SH0ES data from the entire dataset to constrain the parameters of novel models. We observe that the constraints on $H_0$ from two coupling models are slightly higher than that from the $Λ$CDM model, but they exhibit a significant inconsistency with the SH0ES data, consistent with prior research findings in the EDE model. Subsequently, we incorporate SH0ES data to re-constrain the parameters of various models, our findings reveal that both coupling models yield best-fit values for $H_0$ approximately around $72.23$ km/s/Mpc, effectively mitigating the Hubble tension. Similar to the EDE model, the coupling models yield the $S_8$ values that still surpasses the result of the $Λ$CDM model. Nevertheless, the best-fit values for $S_8$ obtained with the two new models are 0.8192 and 0.8177, respectively, which are lower than the 0.8316 achieved by the EDE model. Consequently, although our coupling models fail to fully resolve the large-scale structure tension, they partially mitigate the adverse effect of the original EDE model.

14 pages, 9 figures. In this replacement, we have amalgamated the original content of this manuscript with that of a previous paper [arXiv:2310.09798]. arXiv admin note: substantial text overlap with arXiv:2310.09798