This paper presents an experimental study of a driven Kerr oscillator with two-fold degeneracies in its spectrum, which can be controlled by adjusting the frequency of a squeezing drive. The oscillator is subjected to a three-wave mixing process that, in combination with the Kerr interaction, creates an effective static two-well potential in phase space rotating at half the frequency of the sinusoidal drive. These degeneracies can be turned on and off, and their number can be adjusted by changing the squeezing drive frequency. When the detuning Δ between the oscillator frequency and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, the oscillator exhibits m + 1 exact, parity-protected, spectral degeneracies that are insensitive to the squeezing drive amplitude. These degeneracies arise from destructive interference of tunnel paths in the classically forbidden region of the double-well potential. The experiment demonstrates a protected cat qubit in the ground state manifold of the oscillator, showing a peaked enhancement of the incoherent well-switching lifetime. The results highlight the relationship between degeneracies and noise protection in a driven quantum system. The study also shows that the degeneracies are not limited to the ground state but also occur in the excited state manifolds. The experiment demonstrates the ability to control the number and activation of these degeneracies, and identifies the drive frequency as a critical control parameter. The results show that the degeneracies lead to an exponential reduction of tunnel splitting in both ground and excited states of the oscillator, enabling a protected cat-qubit. The study also demonstrates the continuous Z-gate operation for cat qubits, adding valuable capability to the single qubit gate-set for quantum computation. The findings provide experimental evidence of the cancellation of tunneling due to interference in the classically forbidden region.This paper presents an experimental study of a driven Kerr oscillator with two-fold degeneracies in its spectrum, which can be controlled by adjusting the frequency of a squeezing drive. The oscillator is subjected to a three-wave mixing process that, in combination with the Kerr interaction, creates an effective static two-well potential in phase space rotating at half the frequency of the sinusoidal drive. These degeneracies can be turned on and off, and their number can be adjusted by changing the squeezing drive frequency. When the detuning Δ between the oscillator frequency and the second subharmonic of the drive equals an even multiple of the Kerr coefficient K, the oscillator exhibits m + 1 exact, parity-protected, spectral degeneracies that are insensitive to the squeezing drive amplitude. These degeneracies arise from destructive interference of tunnel paths in the classically forbidden region of the double-well potential. The experiment demonstrates a protected cat qubit in the ground state manifold of the oscillator, showing a peaked enhancement of the incoherent well-switching lifetime. The results highlight the relationship between degeneracies and noise protection in a driven quantum system. The study also shows that the degeneracies are not limited to the ground state but also occur in the excited state manifolds. The experiment demonstrates the ability to control the number and activation of these degeneracies, and identifies the drive frequency as a critical control parameter. The results show that the degeneracies lead to an exponential reduction of tunnel splitting in both ground and excited states of the oscillator, enabling a protected cat-qubit. The study also demonstrates the continuous Z-gate operation for cat qubits, adding valuable capability to the single qubit gate-set for quantum computation. The findings provide experimental evidence of the cancellation of tunneling due to interference in the classically forbidden region.