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In this paper, the author considers twisted <i>q</i>-analogues of Catalan-Daehee numbers and polynomials by using <i>p</i>-adic <i>q</i>-integral on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="double-struck">Z</mi><mi>p</mi></msub></semantics></math></inline-formula>. We derive some explicit identities for those twisted numbers and polynomials related to various special numbers and polynomials.