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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 thetotal space of the fibration $ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\timesAdS_{F}^{2} $. After the projective module description of this bundle, thepseudo fuzzy Dirac and chirality operators on fuzzy $ AdS^{2}_{F}\timesAdS_{F}^{2} $ have been studied. Using the fuzzy Ginsparg-Wilson algebra, ithas been studied the gauged fuzzy Dirac and chirality operators in instantonsector. It has been showed that they have correct commutative limit in thelimit case when noncommutative parameter $ l_{\alpha} $ tends to infinity.

Fuzzy AdS-conifold $ Y_{AdS_{F}}^{6} $ and Dirac operator of principal fibration $ X_{AdS_{F}}^{5}\rightarrow AdS_{F}^{2}\times AdS_{F}^{2} $