Integrated optical microresonators exploiting either second-order (
χ(2)) or third-order (
χ(3)) nonlinearities have become key platforms for frequency conversion, low-noise microwave photonics, and quantum entanglement generation. Here, we present an analytic theory of Kerr-enhanced three-wave mixing amplification in an electro-optic microresonator with both
χ(2) and
χ(3) nonlinearities. We demonstrate that Kerr dressing hybridizes the optical sidebands, renormalizing the
χ(2) couplings and detunings. As a result the system exhibits gain in regions where analogous bare
χ(2) or
χ(3) amplifiers are subthreshold. Time-domain Langevin simulations confirm this threshold reduction, mapping a practical design window for experiments.
We demonstrate bright two-mode squeezed states generated in silicon nitride microresonators using integrated seed-assisted optical parametric amplification (OPA). This integrated quantum source produces a bright squeezed quantum frequency comb spanning multiple mode pairs with frequency separations up to 11 THz, and achieves up to 5.6 dB of measured intensity-difference squeezing. We systematically explore how pump and seed detunings, gain and phase-matching conditions of nonlinear interaction influence squeezing performance. These factors extend beyond conventionally known squeezed-state-degradation with optical losses, impacting the achievable squeezing in integrated microresonators. These insights advance the fundamental understanding necessary for practical integrated quantum photonic devices, paving the way toward robust, scalable applications in quantum information processing and quantum-enhanced sensing.