The Varanasi-Allahabad line via Manduadih was initially an MG line while the MGS-BSB-LKO line was always BG.
The MG line coming from Mau and going towards Allahabad was an independent MG line. So, BSB was initially two stations in the same complex, a BG one and an MG one. The MG portion was handled by NER and the BG portion by NR. This is what is called a 'Joint Station', where two different railway zones use the same station. The station building will belong to one zone only, but there will be...
more... an agreement between the two zones as to the maintenance and other aspects of the station.