Characterizing the climates of exoplanets— planets orbiting other stars —advances our knowledge of atmospheric science, planetary formation, internal structures and will eventually lead to the holy grail of exoplanet science, detecting biosignatures of alien life. This study focuses on atmospheric convection in super-Earth and sub-Neptune exoplanets, a relatively unexplored topic. We aim to understand how compositional gradients of atmospheric tracers affect stable atmospheric states, the distribution of atmospheric tracers, and cloud formation. We use 3D convection resolving simulations with Cloud Model 1 (CM1) to build a fundamental understanding of how compositional variations influence convection and the atmospheric state in both hydrogen-dominated and higher mean molecular weight exoplanet atmospheres. We perform modular, idealized simulations with CM1 to study compositional convection. Initially, we examine compositional convection in non-condensing atmospheres without the effects of radiation or other planetary processes. Next, we run simulations where atmospheric tracers can condense, thus incorporating the effect of latent heat release on compositional convection. Lastly, we use CM1 to model a radiative-convective system. Our simulations aim to identify stable atmospheric structures, determine how convection distributes atmospheric tracers, and explore the impact on convective clouds. The CM1 simulation results pave the way for future developments of convection parameterizations for global climate modeling of sub-Neptune and super-Earth exoplanet atmospheres.