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The aim of this work is to analyze the relative controllability and Ulamn–Hyers stability of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo mathvariant="sans-serif">ψ</mo></semantics></math></inline-formula>-Caputo fractional neutral delay differential system. We use neutral <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo mathvariant="sans-serif">ψ</mo></semantics></math></inline-formula>-delayed perturbation of the Mitttag–Leffler matrix function and Banach contraction principle to examine the Ulam–Hyers stability of our considered system. We formulate the Grammian matrix to establish the controllability results of the linear fractonal differential system. Further, we employ the fixed-point technique of Krasnoselskii’s type to establish the sufficient conditions for the relative controllability of a semilinear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo mathvariant="sans-serif">ψ</mo></semantics></math></inline-formula>-Caputo neutral fractional system. Finally, the theoretical study is validated by providing an application.