In this paper, a dataset of wall-resolved large-eddy simulations of cryogenic hydrogen at supercritical pressure and different values of wall heat flux is presented. The aim is to provide a reference dataset for wall-function development under trans- and supercritical conditions, such as those found in liquid rocket engine applications. The employed numerical framework is a pressure-based segregated low-Mach-number approach based on an equation-of-state independent formulation. The wall-adapting local eddy-viscosity subgrid model is used for turbulence closure. Real-gas effects are taken from the National Institute for Standards and Technology database and stored as a function of a nondimensional temperature at the considered pressure. A validation and a grid-convergence analysis are first performed on an incompressible case without imposed heat flux. The effect of axial, radial, and azimuthal refinements on first- and second-order velocity statistics is discussed and compared with direct numerical simulation data from the literature. A parametric analysis at different wall heat fluxes is then performed by keeping the inlet mass flux, temperature, and Reynolds number constant. Particular attention is devoted to turbulent pseudoboiling and its effect on the wall temperature. The latter shows a more pronounced increment as the heat flux increases, which is attributed to the pseudochange of the phase in the core flow. Correspondingly, a flattening of the probability density function of the temperature is observed, and it is associated with the pseudoboiling interface forming close to the wall and causing a more intense stratification. First- and second-order statistics for velocity and selected scalars are then presented, and the effect of pseudoboiling is discussed. The effect of the wall heat flux on the viscous and thermal resolution of the computational grid is also assessed, and considerations on the relation between turbulent pseudoboiling and near-wall gradients is finally provided.