We investigate the influence of ram pressure on the star-formation rate and the distribution of gas and stellar matter in interacting model galaxies in clusters. To simulate the baryonic and non-baryonic components of interacting disc galaxies moving through a hot, thin medium, we use a combined N-body/hydrodynamic code gadget2 with a description for star formation based on density thresholds. Two identical model spiral galaxies on a collision trajectory with three different configurations were investigated in detail. In the first configuration, the galaxies collide without the presence of an ambient medium. In the second configurations, the ram pressure acts face-on on the interacting galaxies and in the third configuration the ram pressure acts edge-on. The ambient medium is thin (10−28 g cm−3), hot (3 keV ≈ 3.6 × 107 K) and has a relative velocity of 1000 km s−1, to mimic an average low ram pressure in the outskirts of galaxy clusters. The interaction velocities are comparable to galaxy interactions in groups, falling along filaments into galaxy clusters. The global star-formation rate of the interacting system is enhanced in the presence of ram pressure by a factor of 3 in comparison to the same interaction without the presence of an ambient medium. The tidal tails and the gaseous bridge of the interacting system are almost completely destroyed by the ram pressure. The amount of gas in the wake of the interacting system is ∼50 per cent of the total gas of the colliding galaxies after 500 Myr the galaxies start to feel the ram pressure. Nearly ∼10–15 per cent in mass of all newly formed stars are formed in the wake of the interacting system at distances larger than 20 kpc behind the stellar discs. As the tidal tails and the gaseous bridge between the interacting systems feel the ram pressure, knots of cold gas (T < 1 × 105 K) start to form. These irregular structures contain several 106 M⊙ of cold gas and newly formed stars and, as the ram pressure acts on them, they move far away (several 100 kpc) from the stellar discs. They can be classified as ‘stripped baryonic dwarf’ galaxies. These ‘stripped baryonic dwarfs’ are strongly affected by turbulence, for example Kelvin–Helmholtz instabilities, which are not resolvable within the presented smoothed particle hydrodynamics simulations. Heat conduction, which is not included, would affect these small structures as well. Therefore, we give some estimate on the lifetime of these objects.