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 $\kappa=\aleph_\kappa$ .