Generalizing the notion of local $\phi$-symmetry of Takahashi, in the present paper, we introduce the notion of local $\phi$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $\phi$-semisymmetry of a Sasakian manifold and obtain its characterization. It is shown that the local $\phi$-semisymmetry, local projective $\phi$-semisymmetry and local concircular $\phi$-semisymmetry are equivalent. It is also shown that local conformal $\phi$-semisymmetry and local conharmonical $\phi$-semisymmetry are equivalent.
Categories: math.DG