The exciton dynamics of model aggregate systems, dimer, trimer, and pentamer, composed of two-state monomers is computationally investigated in the presence of three types of quantized optical fields, i.e., coherent, amplitude-squeezed, and phase-squeezed fields, in comparison with the case of classical laser fields. The constituent monomers are assumed to interact with each other by the dipole-dipole interaction, and the two-exciton model, which takes into account both the one- and two-exciton generations, is employed. As shown in previous studies, near-degenerate exciton states in the presence of a (near) resonant classical laser field create quantum superposition states and thus cause the spatial exciton recurrence motion after cutting the applied field. In contrast, continuously applied quantized optical fields turn out to induce similar exciton recurrence motions in the quiescent region between the collapse and revival behaviors of Rabi oscillation. The spatial features of exciton recurrence motions are shown to depend on the architecture of aggregates. It is also found that the coherent and amplitude-squeezed fields tend to induce longer-term exciton recurrence behavior than the phase-squeezed field. These features have a possibility for opening up a novel creation and control scheme of exciton recurrence motions in aggregate systems under the quantized optical fields.