Two measurements related to the proton and antiproton production near midrapidity in $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV Au+Au collisions using the STAR detector at the Relativistic Heavy Ion Collider (RHIC) are discussed. At intermediate impact parameters, the net-proton midrapidity d$v_1$/d𝑦, where $v_1$ and 𝑦 are directed flow and rapidity, respectively, shows non-monotonic variation as a function of beam energy. This non-monotonic variation is characterized by the presence of a minimum in d$v_1$/d𝑦 between $\sqrt{s_{NN}}$ = 11.5 and 19.6 GeV and a change in the sign of d$v_1$/d𝑦 twice between $\sqrt{s_{NN}}$ = 7.7 and 39 GeV. At small impact parameters the product of the moments of net-proton distribution, kurtosis × variance ($\kappa \sigma^2$) and skewness × standard deviation ($S\sigma$) are observed to be significantly below the corresponding measurements at large impact parameter collisions for $\sqrt{s_{NN}}$ = 19.6 and 27 GeV. The $\kappa \sigma^2$ and $S\sigma$ values at these beam energies deviate from the expectations from Poisson statistics and that from a hadron resonance gas model. Both these measurements have implications towards understanding the quantum chromodynamics (QCD) phase structures, the first-order phase transition and the critical point in the high baryonic chemical potential region of the phase diagram.