Maintaining both high sensitivity and large figure of merit (FoM) is crucial in regard to the performance of optical devices, particularly when they are intended for use as biosensors with extremely low limit of detection (LoD). Here, a stack of nano-assembled layers in the form of 1D photonic crystal, deposited on D-shaped single-mode fibers, is created to meet these criteria, resulting in the generation of Bloch surface wave resonances. The increase in the contrast between high and low refractive index (RI) nano-layers, along with the reduction of losses, enables not only to achieve high sensitivity, but also a narrowed resonance bandwidth, leading to a significant enhancement in the FoM. Preliminary testing for bulk RI sensitivity is carried out, and the effect of an additional nano-layer that mimics a biological layer where binding interactions occur is also considered. Finally, the biosensing capability is assessed by detecting immunoglobulin G in serum at very low concentrations, and a record LoD of 70 aM is achieved. An optical fiber biosensor that is capable of attaining extraordinarily low LoD in the attomolar range is not only a remarkable technical outcome, but can also be envisaged as a powerful tool for early diagnosis of diseases.