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We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of (h,q)-Genocchi polynomials. We define the Cangul-Ozden-Simsek's type twisted (h,q)-Genocchi polynomials and numbers. We also have the generalized twisted (h,q)-Genocchi numbers attached to the Dirichlet's character χ. Finally, we define zeta functions related to (h,q)-Genocchi polynomials and have the generating function of the generalized (h,q)-Genocchi numbers attached to χ.