This paper presents a radar target tracking framework for addressing main-beam range deception jamming attacks using random finite sets (RFSs). Our system handles false alarms and detections with false range information through multiple hypothesis tracking (MHT) to resolve data association uncertainties. We focus on range gate pull-off (RGPO) attacks, where the attacker adds positive delays to the radar pulse, thereby mimicking the target trajectory while appearing at a larger distance from the radar. The proposed framework incorporates knowledge about the spatial behavior of the attack into the assumed RFS clutter model and uses only position information without relying on additional signal features. We present an adaptive solution that estimates the jammer-induced biases to improve tracking accuracy as well as a simpler non-adaptive version that performs well when accurate priors on the jamming range are available. Furthermore, an expression for RGPO attack detection is derived, where the adaptive solution offers superior performance. The presented strategies provide tracking resilience against multiple RGPO attacks in terms of position estimation accuracy and jamming detection without degrading tracking performance in the absence of jamming.