Is the consistency of the following well-known:
$(*)$: There exists a singular cardinal $\kappa$ such that :
(1) $\kappa$ is a Jonsson cardinal,
(2) $\kappa$ is not a fixed point of the $\aleph-$function, i.e., $\kappa < \aleph_\kappa.$
If we remove the second assumption, then the answer is easy:
(A): Prikry forcing over a measurable cardinal $\kappa,$ turns $\kappa$ into a singular Jonsson cardinal, but $\kappa=\aleph_\kappa$ in such a model.
(B): If $κ$ is a singular limit of measurable cardinals, then $κ$ is Jonsson, but again $\kappa=\aleph_\kappa$ .