We demonstrate the emergence of novel topological phases in quantum Hall-superconductor hybrid structures driven by Landau-level mixing and spin-orbit coupling. For a narrow superconducting stripe atop a two-dimensional electron gas, hybridization of chiral Andreev edge states yields a rich phase diagram, including the unexpected realization of the long-sought $p$-wave superconducting state at even filling factors, thus allowing its detection at lower fields. These phases feature quantized nonlocal conductance from electron cotunneling at filling factor $\nu =1$, coexisting with quantized crossed Andreev reflection at $\nu =2$ leading to the appearance of a neutral mode. Numerical simulations and effective modeling reveal how spin-orbit coupling and geometry control these transitions, enabling realistic routes to engineer topology in proximized quantum Hall devices.

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• Landau levels
• Quantum Hall effect
• Topological superconductors
• Nanostructures