\vspace{6pt} \begin{center} \atitle{Production of light nuclei in Au+Au collisions with the STAR BES-II program} \vspace{12pt} \authors{Sibaram Behera$^1$ and Yixuan Jin$^2$} \\(for the STAR Collaboration) \vspace{6pt} \affiliation{$^1$Indian Institute of Science Education and Research (IISER) Tirupati, India \\ $^2$Central China Normal University (CCNU), China} \end{center} \vspace{24pt} The production mechanism of light (anti-)nuclei in heavy-ion collisions can be either by the thermal model or the coalescence model. By studying the yields and ratios of light (anti-)nuclei, we can gain insight into their production mechanism and physical properties of the expanding system at freeze-out. Furthermore, the enhancement in the light nuclei compound ratios such as $N_{t}N_{p}/N_{d}^{2}$ and $N_{^3He}N_{p}/N_{d}^{2}$ from the coalescence baseline, has been suggested as a potential probe to search for the critical phenomena in the QCD phase diagram. This enhancement might be a consequence of the enhanced baryon density fluctuations when the system is in vicinity of the critical point or the first-order phase transition. In the first phase of the Beam Energy Scan (BES-I) program at RHIC, an enhancement relative to the coalescence baseline of the light nuclei yield ratio ($N_{t}N_{p}/N_{d}^{2}$) is observed in the most central Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 and 27 GeV with a combined significance of 4.1$\sigma$. The large datasets ($\sim 10\times$BES-I) taken by the STAR BES-II with enhanced detector capabilities will greatly improve the precision of the new measurements. In this talk, we will present the centrality and energy dependence of transverse momentum ($p_T$) spectra of $p$, $\bar p$, $d$, $\bar d$, and $^{3}He$ in Au+Au collisions at BES-II energies of $\sqrt{s_{NN}}$ = 7.7 -- 27 GeV. We will also report the centrality and energy dependence of integrated particle yields ($dN/dy$) and mean $p_{T}$ ($\langle p_{T} \rangle$) of light nuclei. We will discuss the centrality and $p_T$ dependence of the coalescence parameters ($B_{2}(d)$ and $B_{3}(^3He)$). The physics implications of these results will be discussed.