Most widely used dielectrics for MLCC are based on BaTiO₃ composition which inevitably shows performance degradation during the application due to the migration of oxygen vacancies ($V_{\mathrm{o}}^{\cdot \cdot }$). Here, the BaTiO₃, (${\text{Ba}}_{0.97}$${\text{Ca}}_{0.03}$)TiO₃, Ba(${\text{Ti}}_{0.98}$${\text{Mg}}_{0.02}$)O₃, (${\text{Ba}}_{0.97}$${\text{Ca}}_{0.03}$)(${\text{Ti}}_{0.98}$${\text{Mg}}_{0.02}$)O₃, (${\text{Ba}}_{0.96}$${\text{Ca}}_{0.03}$${\text{Dy}}_{0.01}$)(${\text{Ti}}_{0.98}$${\text{Mg}}_{0.02}$)O₃ ceramics (denoted as BT, BCT, BTM, BCTM and BCDTM, respectively) were prepared by a solid-state reaction method. The core-shell structured grains ($\sim$200 nm) featured with 10-20 nm wide shell were observed and contributed to the relatively flat dielectric constant-temperature spectra of BTM, BCTM and BCDTM ceramics. The TSDC study found that the single/ mix doping of Ca${}^{2+}$, especially the Mg${}^{2+}$, Mg${}^{2+}$/Ca${}^{2+}$ and Mg${}^{2+}$/Ca${}^{2+}$/Dy${}^{3+}$ could limit the emergence of $V_{\mathrm{o}}^{\cdot \cdot }$ during the sintering and suppress its long-range migration under the electric-field. Because of this, the highly accelerated lifetimes of the ceramics were increased and the value of BCDTM is 377 times higher than that of BT ceramics. The $p-n$ junction model was built to explain the correlation mechanism between the long-range migration of $V_{\mathrm{o}}^{\cdot \cdot }$ and the significantly increased leakage current of BT-based dielectrics in the late stage of HALT.