In cuprate superconductors with high critical transition temperature (T_c), light hole-doping to the parent compound, which is an antiferromagnetic Mott insulator, has been predicted to lead to the formation of small Fermi pockets. These pockets, however, have not been observed. Here, we investigate the electronic structure of the five-layered Ba₂Ca₄Cu₅O₁₀(F,O)₂, which has inner copper oxide (CuO₂) planes with extremely low disorder, and find small Fermi pockets centered at (π/2, π/2) of the Brillouin zone by angle-resolved photoemission spectroscopy and quantum oscillation measurements. The d-wave superconducting gap opens along the pocket, revealing the coexistence between superconductivity and antiferromagnetic ordering in the same CuO₂ sheet. These data further indicate that superconductivity can occur without contribution from the antinodal region around (π, 0), which is shared by other competing excitations.