Transitions from bound states in the continuum (BICs) to quasi-BICs ($q\mathrm{BICs}$) are typically realized by introducing in-plane asymmetry, including permittivity asymmetry (ε-qBICs) and geometry asymmetry ($\mathrm{g}\text{−}q\mathrm{BICs}$). Here, we demonstrate that when the in-plane symmetry is rigorously kept, the transition can also occur, provided the out-of-plane asymmetry is designed, which is called ${\sigma }_h\text{−}q\mathrm{BICs}$ in this work. When the ${\sigma }_h$ symmetry is gradually broken and exceeds a certain threshold, the system undergoes a transition from BIC to qBIC. During the process, a topological phase transition characterized by a Zak phase inversion accompanied by a band inversion appears. This process not only enables controlled radiation coupling of BICs but also introduces a defect-immune $q\mathrm{BIC}$ regime. Our findings establish a general mechanism for engineering high-$Q$ resonances and topologically robust plasmonic cavities.

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• Bound states in the continuum
• Nanophotonics
• Phononic crystals
• Plasmonics
• Topological effects in photonic systems
• Topological metamaterials