We construct examples of deformed Hermitian Yang–Mills connections and deformed \(\textrm{Spin}(7)\) -instantons (also called \(\textrm{Spin}(7)\) deformed Donaldson–Thomas connections) on the cotangent bundle of \(\mathbb {C}\mathbb {P}^2\) endowed with the Calabi hyperKähler structure. Deformed \(\textrm{Spin}(7)\) -instantons on cones over 3-Sasakian 7-manifolds are also constructed. We show that these can be used to distinguish between isometric structures and also between \(\textrm{Sp}(2)\) and \(\textrm{Spin}(7)\) holonomy cones. To the best of our knowledge, these are the first non-trivial examples of deformed \(\textrm{Spin}(7)\) -instantons.
