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In this note, we study skew cyclic and skew constacyclic codes over the mixed alphabet <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo>=</mo><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><msub><mi mathvariant="script">R</mi><mn>1</mn></msub><msub><mi mathvariant="script">R</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>q</mi><mo>=</mo><msup><mi>p</mi><mi>m</mi></msup><mo>,</mo></mrow></semantics></math></inline-formula> p is an odd prime with <i>m</i> odd and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>1</mn></msub><mo>=</mo><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>u</mi><mn>2</mn></msup><mo>=</mo><mi>u</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>2</mn></msub><mo>=</mo><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>+</mo><mi>u</mi><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>+</mo><mi>v</mi><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>u</mi><mn>2</mn></msup><mo>=</mo><mi>u</mi><mo>,</mo><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mi>v</mi><mo>,</mo><mi>u</mi><mi>v</mi><mo>=</mo><mi>v</mi><mi>u</mi><mo>=</mo><mn>0</mn><mo>.</mo></mrow></semantics></math></inline-formula> Such codes consist of the juxtaposition of three codes of the same size over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="double-struck">F</mi><mi>q</mi></msub><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">R</mi><mn>1</mn></msub><mo>,</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">R</mi><mn>2</mn></msub></semantics></math></inline-formula>, respectively. We investigate the generator polynomial for skew cyclic codes over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">R</mi></semantics></math></inline-formula>. Furthermore, we discuss the structural properties of the skew cyclic and skew constacyclic codes over <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">R</mi><mo>.</mo></mrow></semantics></math></inline-formula> We also study their <i>q</i>-ary images under suitable Gray maps.