Bit-patterned media recording (BPMR) is a promising technology for increasing the areal density (AD) of magnetic data storage systems. In BPMR, the non-magnetic zone is reduced to increase AD, which causes serious problems such as two-dimensional (2D) interference and track mis-registration (TMR). Therefore, in previous studies, a serial detection, which exploits the Viterbi algorithm (VA), was proposed to combat 2D interference. Because the VA lacks prior information from the inner detector to the outer detector, in this study, we use the maximum a posteriori (MAP) algorithm to supply prior information from the inner detector to the outer detector. Simulation results show that the proposed model can improve the bit error ratio (BER) performance of serial detection, especially in cases where the BPMR suffers from TMR effects.