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Stably stratified layers may be present at the top of the electrically conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double‐diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800 km‐thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy‐driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e., weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet‐like structures that are elongated in the meridional direction. The azimuthal size decreases when the thermal stratification increases, following closely the scaling law expected from the linear planar theory (Stern, 1960, https://doi.org/10.1111/j.2153-3490.1960.tb01295.x). We find that the radial flows always remain laminar with local Reynolds number of order 1–10. Equatorially symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non‐axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields. Convection occurs in planetary interiors due to local changes of density, which can be produced by changes of temperature or chemical composition. In particular, convection occurs in the electrically conducting fluid layers located deep inside planets and is at the origin of the generation of planetary magnetic fields. However, for many planets, the upper part of this electrically conducting region might not be subject to standard convection because the gradients of either temperature or chemical composition produce a further increase of the density with depth, leading to the formation of a stable layer. In some cases, the gradients of these two components act in opposition. Such might be the case of the upper part of Mercury's core, where the stable layer is maintained by the thermal gradient, but the compositional gradient is unstable. This situation is prone to fingering convection, where fluid instabilities release the potential energy associated with the compositional gradient. Here we show that fingering convection consists of sheet‐like flows with a narrow longitudinal size of approximately 1 m in Mercury‐like conditions. Strong zonal (i.e., east/westward) flows also form. The presence of fingering convection in stable layers might have important consequences for the magnetic fields observed at the planet's surface. Fingering convection in a Mercury‐like stable layer produces thin sheet‐like radial flows that are elongated in the meridional directionThe radial flows are always laminar and their azimuthal length is expected to be about 1 m in planetary coresStrong zonal flows form as a by‐product of the latitudinal variations of the composition transport Fingering convection in a Mercury‐like stable layer produces thin sheet‐like radial flows that are elongated in the meridional direction The radial flows are always laminar and their azimuthal length is expected to be about 1 m in planetary cores Strong zonal flows form as a by‐product of the latitudinal variations of the composition transport