Binary Offset Carrier (BOC) modulation is used in the Global Navigation Satellite System (GNSS). Unlike Binary Phase Shift Keying (BPSK) in the Global Positioning System, BOC-modulated signals have side-peaks in the autocorrelation function (ACF) leading to positioning errors in multipath channels. This paper introduces a two-stage BOC first arrival path detection network (BOC-FPDNet). This includes side-peaks cancellation (SC) and multipath time delay estimation (MDE) for BOC modulation. The SC is a deep learning-based method that cancels side-peaks without added computational load or noise increase. The MDE uses Multi-head attention to extract ACF output features and consists of two heads , positive and negative sample detector, for time delay estimation. The effectiveness of BOC-FPDNet is demonstrated by comparing it to super-resolution and other deep learning detection techniques in various multipath channel simulations and real urban data. Results show BOC-FPDNet provides superior side-peak cancellation and accurate BOC-modulated signal detection.