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We construct $Spin(7)$-instantons on one of Joyce's compact$Spin(7)$-manifolds. The underlying compact $Spin(7)$-manifold given by Joyceis the same as in Lewis' construction of $Spin(7)$-instantons. However, ourconstruction method and the resulting instantons are new. The compact$Spin(7)$-manifold is constructed by gluing a $Spin(7)$-orbifold and certainlocal model spaces around the orbifold singularities. We construct ourinstantons by gluing non-flat connections on the local model spaces to a flatconnection on the $Spin(7)$-orbifold. We deliver more than $20,000$ exampleswithin the structure groups $SO(3), SO(4), SO(5), SO(7)$, and $SO(8)$.

Spin(7)-instantons on Joyce's first examples of compact Spin(7)-manifolds