Quantum computing brings opportunities in the field of cybersecurity, yet ensuring that quantum security software is actually functional is a task of great proportions. This paper provides QuSecVerify, a verification model tailored to quantum cybersecurity applications (such as quantum key distribution, quantum-based intrusion detection, and quantum blockchain applications). We have used three methods that include formal verification over SMT solvers over a Quantum RAM model, mutation testing over security-oriented fault operators, and statistical testing as defined by repeated quantum measurements. We benchmarked the framework on key distribution on a quantum machine learning intrusion detector, BB84, and quantum consensus protocol. Our findings indicate that using our approach identifies 95.7 percent of injected faults, which is 40 percent less verification than in manual verifiability, and 23 bugs were still detected in tested implementations. The work is a bridge in the field of quantum software engineering, as it offers a practical and general tool to verify quantum code that is security-critical