Ram-pressure stripping (RPS) is a well observed phenomenon of massive spiral galaxies passing through the hot intra-cluster medium (ICM) of galaxy clusters. For dwarf galaxies (DGs) within a cluster, the transformation from gaseous to gas-poor systems by RPS is not easily observed and must happen in the outskirts of clusters. In a few objects in close by galaxy clusters and the field, RPS has been observed. Since cluster early-type DGs also show a large variety of internal structures (unexpected central gas reservoirs, blue stellar cores, composite radial stellar profiles), we aim in this study to investigate how ram pressure (RP) affects the interstellar gas content and therefore the star-formation (SF) activity. Using a series of numerical simulations, we quantify the dependence of the stripped-off gas on the velocity of the infalling DGs and on the ambient ICM density. We demonstrated that SF can be either suppressed or triggered by RP depending on the ICM density and the DGs mass. Under some conditions, RP can compress the gas, so that it is unexpectedly retained in the central DG region and forms stars. When gas clouds are still bound against stripping but lifted from a thin disk and fall back, their new stars form an ellipsoidal (young) stellar population already with a larger velocity dispersion without the necessity of harassment. Most spectacularly, star clusters can form downstream in stripped-off massive gas clouds in the case of strong RP. We compare our results to observations.