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We present the design, configuration, and performance characterization of a scalable readout system based on the BETA application-specific integrated circuit (ASIC), developed to meet stringent requirements on noise, linearity, dynamic range, and power consumption for multi-channel silicon photomultiplier (SiPM) detectors in spaceborne instrumentation. The readout electronics consists of modular interface boards (FIBs) hosting multiple BETA ASICs and controlled by a field-programmable gate array (FPGA), which provides configuration, data acquisition, and global trigger generation. Multiple BETA FIBs were tested in a dedicated optical setup enabling simultaneous readout of a large number of channels. The system performance was evaluated using three S13552-10 SiPM arrays manufactured by Hamamatsu for the FIT detector, a scintillating-fiber tracker developed for charged cosmic-ray particle tracking and charge measurement in the HERD mission. We describe the configuration procedures and performance measurements of the readout system, including gain calibration, linearity characterization, and threshold response. In addition, we present the development of a global internal trigger logic for the identification of ionizing particles in the FIT detector. The results demonstrate the stability, scalability, and suitability of the developed BETA-based readout system for large-scale multi-channel SiPM detector applications in space experiments.