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We define the signed Cayley graph on Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>X</mi><mi>n</mi></msub></semantics></math></inline-formula> denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>, and study several properties such as balancing, clusterability and sign-compatibility of the signed Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>. Apart from it we also study the characterization of the canonical consistency of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>S</mi><mi>n</mi></msub></semantics></math></inline-formula>, for some <i>n</i>.