The ADS124S0x has a one-byte status register that contains flags to indicate if a fault condition has occurred. This byte can be read out from the status register (01h), or can be prepended to each data read as the first byte when reading data from the ADC. To prepend the STATUS byte to each conversion result, set the SENDSTAT bit to 1 in the system control register (09h).
Flags for the PGA output voltage rail monitors and reference monitor are set after each conversion. Reading the STATUS byte reads the flags latched during the last conversion cycle.