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A $\mu$-stable vector bundle $\mathcal{E}$ of rank 2 with $c_1(\mathcal{E}) = 0$ on $ \mathbb{P}^3(C)$ is called mathematical instanton bundle if ${H}^1(\mathbb{P}^3, \mathcal{E}(−2)) = 0$. In this talk, we will study the extended definiton of mathematical instanton sheaves on three-dimensional projective varieties and introduce the concept of rank 0 h-instanton sheaves on them. Specifically, we will focus on the construction of rank 2 h-instanton sheaves on ruled Fano threefolds with Picard rank 2 and index 1. This is a joint work with Marcos Jardim.