As high-end energy systems, including power generation & propulsion, continue to ad- vance, fluid pressure and temperature levels tend to surpass the critical point and enter the supercritical fluid region. Under these conditions, fluids present significant localized alterations in thermophysical properties, which impact the flow dynamics. This can be, for example, strategically harnessed to induce turbulence in microducts, which instead are typically restricted to operate under laminar flow regimes. In turbulent square ducts, the localized anisotropic Reynolds stresses resulting from the fluid interaction with the perpendicular walls imply characteristic flow re-distributions that influence the core flow, known as Prandtl second-kind vortical structures. These streamwise vortical structures manifest near the corners of the duct and impose engineering challenges, such as in the prediction of pressure-drop and heat transfer. Therefore, this work aims to characterize the dynamics of secondary flow motions in asymmetrically heated buoyant high-pressure transcritical duct flows at relatively low Reynolds numbers. For a canonical geometry consisting of a microscale square-cross section duct, four cases with different gravity directions will be analyzed using direct numerical simulation (DNS) approaches. The analyses will encompass the examination of first- and second-order flow statistics, energy spectra and two-point correlations, along with the decomposition of the spatio-temporal flow structures using data-driven techniques.