We present a novel high-field optical quantum magnetometer based on saturated absorption spectroscopy on the extreme angular-momentum states of the cesium D2 line. With key features including continuous readout, high sampling rate, and sensitivity and accuracy in the ppm range, it represents a competitive alternative to conventional techniques for measuring magnetic fields of several teslas. The prototype has four small separate field probes, and all support electronics and optics are fitted into a single 19-inch rack to make it compact, mobile, and robust. The field probes are fiber coupled and made from nonmetallic components, allowing them to be easily and safely positioned inside a 7 T MRI scanner. We demonstrate the capabilities of this magnetometer by measuring two different MRI sequences, and we show how it can be used to reveal imperfections in the gradient coil system, to highlight the potential applications in medical MRI. We propose the term EXAAQ (EXtreme Angular-momentum Absorption-spectroscopy Quantum) magnetometry, for this novel method.