(\[twist\]) leads to a deformed Leibniz rule for the deformed SUSY transformations (\[defsusytr\]). This ensures that the $\star$-product of two superfields is again a superfield. Its transformation law is given by $$\begin{aligned}
\delta^\star_\xi ({\rm F}\star {\rm G}) &=& \big(\xi Q 
+ \bar{\xi}\bar{Q} \big) ({\rm F}\star {\rm G}), \label{deftrlaw}\\
&=&
(\delta^\star_\xi {\rm F}) \star {\rm G} 
+ {\rm F} \star (\delta^\star_\xi {\rm G}) \nonumber\\
&& + \frac{i}{2}C^{\alpha\beta}\Big( \bar{\xi}^{\dot{\gamma}}
\sigma^m_{\ \alpha\dot{\gamma}}(\p_m {\rm F})\star (\p_\beta {\rm G}) +
(\p_\alpha {\rm F})\star \bar{\xi}^{\dot{\gamma}}
\sigma^m_{\ \beta\dot{\gamma}}(\p_m {\rm G}) \Big) \label{defLpravilo}\\
&& -\frac{i}{2}\bar{C}_{\dot{\alpha}\dot{\beta}} \Big(
\xi^\alpha\sigma^m_{\
\alpha\dot{\gamma}}\varepsilon^{\dot{\gamma}\dot{\alpha}}(\p_m {\rm F})
\star (\bar{\p}^{\dot{\beta}} {\rm G}) + (\bar{\p}^{\dot{\alpha}} {\rm F})
\star \xi^\alpha\sigma^m_{\ \alpha\dot{\gamma}}
\varepsilon^{\dot{\gamma}\dot{\beta}}(\p_m {\rm G}) \Big) .\nonumber\end{aligned}$$ Note that we have to enlarge the algebra (\[xietaalg\]) by introducing the fermionic derivatives $\p_\alpha$ and $\bar{\p}_{\dot{\alpha}}$. Since these derivatives commute with the generators of Poincar' e algebra $\p_m$ and $M_{mn}$, the super Poincar' e algebra does not change. Especially, the Leibniz rule for $\p_m$ and $M_{mn}$ does not change.

Being interested in a deformation of the Wess-Zumino model, we need to analyze properties of the $\star$-products of chiral fields. A chiral field $\Phi$ fulfills $\bar{D}_{\dot{\alpha}}\Phi =0$, with the supercovariant derivative $\bar{D}_{\dot{\alpha}} = -\bar{\p}_{\dot{\alpha}} -
i\theta^\alpha \sigma^m_{\ \alpha\dot{\alpha}}\p_m$. In terms of component 