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Understanding new superconductors requires high-quality epitaxial thin films to explore intrinsic electromagnetic properties and evaluate device applications^,,,,,,,,. So far, superconducting properties of ferropnictide thin films seem compromised by imperfect epitaxial growth and poor connectivity of the superconducting phase^,,,,. Here we report new template engineering using single-crystal intermediate layers of (001) SrTiO₃ and BaTiO₃ grown on various perovskite substrates that enables genuine epitaxial films of Co-doped BaFe₂As₂ with a high transition temperature (T_c,ρ=0 of 21.5 K, where ρ=resistivity), a small transition width (ΔT_c=1.3 K), a superior critical current density J_c of 4.5 MA cm⁻² (4.2 K) and strong c-axis flux pinning. Implementing SrTiO₃ or BaTiO₃ templates to match the alkaline-earth layer in the Ba-122 with the alkaline-earth/oxygen layer in the templates opens new avenues for epitaxial …