Atomic or molecular preferential adsorption on a surface template provides a facile and feasible means of fabricating ordered low-dimensional nanostructures with tailored functionality for novel applications. In this study, we demonstrate that functionality of C-doped BN nanomesh can be tailored by an external electric field which modifies the strength of the adsorbate binding to the nanomesh. Specifically, selective binding of H, O, H₂, and O₂ at various sites of the C-doped nanomesh—within the pore, on the wire, and at an intermediate site—is investigated with density functional theory. The calculated results find that atomic species are bound, but the molecular species are not bound to the nanomesh. We have shown that it is possible to modify the adsorbate binding energy with the application of an external field, such that the molecular H₂ can be bound at the pore region of the nanomesh. Interestingly, the work function of the nanomesh has a close correlation with the adsorbate binding energy with the BN nanomesh.