  In this paper, we introduce Bar-Natan homology for null homologous links in
\mathbb{RP}^3 over the field of two elements. It is a deformation of the
Khovanov homology in \mathbb{RP}^3 defined by Asaeda, Przytycki and Sikora. We
also define an s-invariant from this deformation using the same recipe as for
links in S^3, and prove some genus bound using it. The key ingredient is the
notion of twisted orientation for null homologous links and cobordisms in
\mathbb{RP}^3.
