Constrained ergodic optimization is a maximizing problem of the ergodic average for a given potential function in the set of all invariant probability measures with a given rotation vector. For symbolic dynamics, we prove that every relative maximizing measure for a generic potential has zero entropy, which is an analogical result of Morris’ theorem for the unconstrained case. In our proof, the density of periodic measures plays a key role. This is joint work with Mao Shinoda.