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 .