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We define an addition signed Cayley graph on a unitary addition Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mi>n</mi></msub></semantics></math></inline-formula> represented by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mo mathvariant="sans-serif">Σ</mo><mi>n</mi><mo>∧</mo></msubsup></semantics></math></inline-formula>, and study several properties such as balancing, clusterability and sign compatibility of the addition signed Cayley graph <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mo mathvariant="sans-serif">Σ</mo><mi>n</mi><mo>∧</mo></msubsup></semantics></math></inline-formula>. We also study the characterization of canonical consistency of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mo mathvariant="sans-serif">Σ</mo><mi>n</mi><mo>∧</mo></msubsup></semantics></math></inline-formula>, for some <i>n</i>.