We present observations of ≳10–100 keV nucleon−1 suprathermal (ST) H, He, O, and Fe ions associated with crossings of the heliospheric current sheet (HCS) at radial distances of <0.1 au from the Sun. Our key findings are as follows: (1) very few heavy ions are detected during the first full crossing, the heavy-ion intensities are reduced during the second partial crossing and peak just after the second crossing; (2) ion arrival times exhibit no velocity dispersion; (3) He pitch-angle distributions track the magnetic field polarity reversal and show up to ∼10:1 anti-sunward, field-aligned flows and beams closer to the HCS that become nearly isotropic farther from the HCS; (4) the He spectrum steepens either side of the HCS, and the He, O, and Fe spectra exhibit power laws of the form ∼E−4–E6; and (5) maximum energies EX increase with the ion's charge-to-mass (Q/M) ratio as ${E}_{X}/{E}_{H}\propto {({Q}_{X}/{M}_{X})}^{\delta }$, where δ ∼ 0.65–0.76, assuming that the average Q states are similar to those measured in gradual and impulsive solar energetic particle events at 1 au. The absence of velocity dispersion in combination with strong field-aligned anisotropies closer to the HCS appears to rule out solar flares and near-Sun coronal-mass-ejection-driven shocks. These new observations present challenges not only for mechanisms that employ direct parallel electric fields and organize maximum energies according to E/Q but also for local diffusive and magnetic-reconnection-driven acceleration models. Reevaluation of our current understanding of the production and transport of energetic ions is necessary to understand this near-solar, current-sheet-associated population of ST ions.