Boundedness of certain linear operators on twisted Fock spaces

On the twisted Fock spaces $\mathcal{F}^\lambda(\mathbb{C}^{2n})$ we consider two types of convolution operators $S_\varphi$ and $\widetilde{S}_\varphi$ associated to an element $\varphi \in \mathcal{F}^\lambda(\mathbb{C}^{2n}) .$ We find a necessary and sufficient condition on $\varphi$ so that $S_\varphi$ (resp. $\widetilde{S}_\varphi$ ) is bounded on $\mathcal{F}^\lambda(\mathbb{C}^{2n}).$ We show that for any given non constant $\varphi$ at least one of these two operators is unbounded.