Photomultiplication-type organic photodetectors (PM-OPDs) provide for signal amplification, ideal for detecting faint light, and simplifying detection systems. However, current designs often suffer from slow response speed and elevated dark current. Conversely, photovoltaic-type organic photodetectors (PV-OPDs) provide fast response and high specific detectivity (D^*) but have limited photoresponse. This study presents the synthesis and incorporation of a non-fullerene acceptor, BFDO-4F, into the active layer to introduce trap states for capturing photogenerated electrons. The resulting device exhibits dual-mode characteristic and is bias-switchable between PV and PM-modes. In PV-mode, the OPDs achieve high D^* of 1.92 × 10¹² Jones and a response time of 2.83/4.43 µs. In PM-mode, the OPDs exhibit exceptional external quantum efficiency (EQE) up to 3484% and a D^* of up to 1.13 × 10¹² Jones. An on-chip self-powered module with PV-mode pixels driving a PM-mode pixel is demonstrated, yielding a photocurrent approximately five times higher than the reference device. This approach paves the way for developing multifunctional bias-switchable dual-mode on-chip OPDs, suitable for various applications.