We study the dynamics of a massless scalar field in hairy black holes within the Einstein-Maxwell-scalar system, computing quasinormal modes (QNMs) using series solution and shooting methods, which show strong agreement. The consistently negative imaginary part confirms stability. Both decay and oscillatory modes increase linearly with the horizon radius, especially for large black holes. Analyzing QNMs across various parameters, we explore their behavior near the small/large black hole phase transition, revealing distinct QNM characteristics that suggest their potential as probes for phase transitions.