implies serious constrains on the vacuum expectation value (vev) of the singlet and the new $U(1)^{\prime}$ gauge coupling $g^{\prime}$.

However, both models have similar form for the scalar potential, where the singlet can play the same role during the EWPT dynamics. In this type of model[^1], the singlet vev within the wrong vacuum could be nonzero, i.e., $\left\langle
S\right\rangle =x\neq 0$, and therefore, is temperature dependant during the EWPT dynamics. This feature could delay the EWPT, i.e., lowers the critical temperature, and enhances the parameters that define the strong first-order phase transition criterion [@SFOPT]: $$\upsilon \left( T_{c}\right) /T_{c}>1,  \label{v/t}$$where $T_{c}$ is the critical temperature and $\upsilon \left( T\right) $ is the temperature dependent scalar vev.

In this work, we will investigate the possibility of getting a strong first-order phase transition within the minimal gauge extension of the MSSM, UMSSM without adding any new field beside the usual singlet.

This paper is organized as follows: in the second section, we give a brief review of the UMSSM model, define the effective potential and discuss different constraints on the parameters. After that, we discuss the EWPT dynamics and show how to get a first-order phase transition. In the fourth section, we discuss 