The relaxation of excitonic polaron and the transport properties in two-dimensional monolayers of transition metal dichalcogenides (TMDCs) such as Mo⁢S2, Mo⁢Se2, W⁢Se2, and W⁢S2 are investigated under the influence of a magnetic barrier and an electric field using the relaxation-time approximation and the Kubo formula. We find that the presence of magnetic barrier strengthens the electron-hole interaction and stabilizes the exciton-polaron while the electric field alters this stability. In addition, exciton-polaron is more relaxed as the electric field increases but due to the magnetic barrier it quickly returns into its equilibrium. Moreover, the electrical conductivity of TMDCs is favored by the electric field and a barrier of high magnetic lengths. Mo⁢Se2 is the compound that presents the highest relaxation time and electrical conductivity. The result indicates that the electrical conductivity grows when the system is relaxed. The thermoelectric power of TMDCs falls when the electric field increases, whereas it does not present a monotonic behavior in the magnetic barrier. It globally decreases for weak values of the magnetic length and enhances for high values. The highest thermoelectricity is obtained in Mo⁢Se2. A high optical conductivity is observed in TMDCs. The result shows that optical transitions rise as the magnetic strength of the barrier increases, but the electric field presents an opposite effect. The probability of absorb energy ℏ⁢�� by the exciton-polaron steps up when the magnetic length and electric field increase. The highest value of optical conductivity and oscillator strength is observed for Mo⁢S2. We demonstrate that the magnetic barrier and electric field are suitable parameters which can be used to improve the performance of TMDCs materials.

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