  It has been constructed fuzzy AdS- conifold $ Y_{AdS_{F}}^{6} $ on the base $
AdS_{F}^{3}\times AdS_{F}^{2} $ which is topologically homeomorphic with the
total space of the fibration $ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times
AdS_{F}^{2} $. After the projective module description of this bundle, the
pseudo fuzzy Dirac and chirality operators on fuzzy $ AdS^{2}_{F}\times
AdS_{F}^{2} $ have been studied. Using the fuzzy Ginsparg-Wilson algebra, it
has been studied the gauged fuzzy Dirac and chirality operators in instanton
sector. It has been showed that they have correct commutative limit in the
limit case when noncommutative parameter $ l_{\alpha} $ tends to infinity.
