We have performed local ferroelectric field effect experiments using an epitaxial heterostructure composed of ferroelectric Pb (Zr_0.2Ti_0.8)O₃ and superconducting Nb doped SrTiO₃, fabricated on an (100)SrTiO₃ substrate by off-axis radio frequency magnetron sputtering and pulsed laser deposition. By switching the polarization field of the 50 nm thick Pb(Zr_0.2Ti_0.8)O₃ layer, we induced a large change in resistivity and a shift of T_c in the 26 nm thick epitaxial Nb doped SrTiO₃ layer. At 270 mK, superconducting on-off switch is realized. Ferroelectric domain array was poled in submicron scale by AFM (Atomic Force Microscope) tip to make a low T_c array in a high T_c superconducting path. A stepwise magnetoresistance was clearly observed in the array device around the T_c. This behavior suggests that 2D superconducting fluctuation induces phase slips and the low T_c array stabilizes them.