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We present a theoretical investigation, based on the tight-binding Hamiltonian, of efficient second- and third-order nonlinear optical processes in the lattice-matched undoped (GaP)N/(Si2)M short-period superlattice that is waveguide-integrated in a microring resonator on an opto-electronic chip. The nonlinear superlattice structures are situated on the optically pumped input area of a heterogeneous “XOI” chip based on silicon. The spectra of χzzz(2)(2ω,ω,ω), χxzx(2)(2ω,ω,ω), χxxxx(3)(3ω,ω,ω,ω) and the Kerr refractive index (n2), have been simulated as a function of the number of the atomic monolayers for “non-relaxed” heterointerfaces; These nonlinearities are induced by transitions between valence and conduction bands. The large obtained values make the (GaP)N/(Si2)M short-period superlattice a good candidate for future high-performance XOI photonic integrated chips that may include Si3N4 or SiC or AlGaAs or Si. Near or at the 810-nm and 1550-nm wavelengths, we have made detailed calculations of the efficiency of second- and third-harmonic generation as well as the performances of entangled photon-pair quantum sources that are based upon spontaneous parametric down conversion and spontaneous four-wave mixing. The results indicate that the (GaP)N/(Si2)M short-period superlattice is competitive with present technologies and is practical for classical and quantum applications.