  We develop the non-normal variations of two classical Prikry-type forcings;
namely, Magidor and Radin forcings. We generalize the fact that the non-normal
Prikry forcing is a projection of the extender-based to a coordinate of the
extender to our forcing and the Radin/Magidor-Radin-extender-based forcing from
\cite{CarmiMagidorRadin,CarmiRadin}.
  Then, we show that both the non-normal variation of Magidor and Radin
forcings can add a Cohen generic function to every limit point of cofinality
$\omega$ of the generic club. Second, we show that this phenomenon is limited
to the cases where the forcings are not designed to change the cofinality of a
measurable $\kappa$ to $\omega_1$. Specifically, in the above-mentioned
circumstances these forcings do not project onto any $\kappa$-distributive
forcing. We use that to conclude that the extender-based Radin/Magidor-Radin
forcing does not add fresh subsets to $\kappa$ as well. In the second part of
the paper we focus on the natural non-normal variation of Gitik's forcing from
\cite[\S3]{GitikNonStationary}. Our main result shows that this poset can be
employed to change the cofinality of a measurable cardinal $\kappa$ to
$\omega_1$ while introducing a Cohen subset of $\kappa$.
