  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 in
fixed-target mode from the second phase of beam energy scan (BES-II) program at
RHIC-STAR. The $v_1$ slopes at mid-rapidity for identified hadrons and
net-particles except $\pi^{+}$ are found to be positive, implying the effect of
dominant repulsive baryonic interactions. The slope of $v_1$ for net-kaon
undergoes a sign change from negative to positive at a lower collision energy
compared to net-proton. An approximate atomic mass number scaling is observed
in the measured $v_1$ slopes of light nuclei at mid-rapidity, which favours the
nucleon coalescence mechanism for the production of light nuclei. The $v_3$
slope for all particles decreases in magnitude with increasing collision
energy, suggesting a notable integrated impact of the mean-field, baryon
stopping, and collision geometry at lower collision energies.
