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We report the measurement of first-order event plane correlated directed flow$(v_1)$ and triangular flow $v_3$ for identified hadrons ($\pi^{\pm}$,$K^{\pm}$, and $p$), net-particle (net-K, net-p), and light nuclei ($d$ and$t$) in Au+Au collisions at $\sqrt{s_{\text{NN}}}$ = 3.2, 3.5, and 3.9 GeV infixed-target mode from the second phase of beam energy scan (BES-II) program atRHIC-STAR. The $v_1$ slopes at mid-rapidity for identified hadrons andnet-particles except $\pi^{+}$ are found to be positive, implying the effect ofdominant repulsive baryonic interactions. The slope of $v_1$ for net-kaonundergoes a sign change from negative to positive at a lower collision energycompared to net-proton. An approximate atomic mass number scaling is observedin the measured $v_1$ slopes of light nuclei at mid-rapidity, which favours thenucleon coalescence mechanism for the production of light nuclei. The $v_3$slope for all particles decreases in magnitude with increasing collisionenergy, suggesting a notable integrated impact of the mean-field, baryonstopping, and collision geometry at lower collision energies.

First-order event plane correlated directed and triangular flow from fixed-target energies at RHIC-STAR