We investigate theoretically two-photon absorption spectroscopy modified by a control field in a confined Y-type four-level system. Dicke-narrowing effect occurs both in two-photon absorption lines and the dips of transparency against two-photon absorption due to enhanced contribution of slow atoms. We also find that the suppression and the enhancement of two-photon absorption can be modified by changing the strength of the control field and the detuning of three laser fields. This control of two-photon absorption may have some applications in information processing and optical devices.