The Radcliffe wave has only recently been recognised as a approx 3\,kpc long coherent gas structure encompassing most of the star-forming regions in the solar vicinity. Since its discovery, it has been mainly studied from the perspective of dynamics, but a detailed chemical study is necessary to understand its nature and the composition of the natal clouds that gave rise to it. For this paper we used some of the connected young open clusters (age lesssim 100 Myr) as tracers of the molecular clouds. We performed high-resolution spectroscopy with GIARPS at the TNG of 53 stars that are bona fide members of seven clusters located at different positions along the Radcliffe wave. We provide radial velocities and atmospheric parameters for all of them. For a subsample consisting of 41 FGK stars, we also studied the chromospheric activity and the content of Li, from which we inferred the age of the parent clusters. These values agree with the evolutionary ages reported in the literature. For these FGK stars, we determined the chemical abundances for 25 species. Pleiades, ASCC\,16, and NGC\,7058 exhibit a solar metallicity while Melotte\,20, ASCC\,19, NGC\,2232, and Roslund\,6 show a slightly subsolar value (approx \,$-$0.1\,dex). On average, the clusters show a chemical composition compatible with that of the Sun, especially for alpha - and Fe-peak elements. Neutron-capture elements, on the other hand, present a slight overabundance of about 0.2\,dex, especially barium. Finally, considering also ASCC\,123, which was studied by our group in a previous research project, we inferred a correlation between the chemical composition and the age or position of the clusters along the wave, demonstrating their physical connection within an inhomogeneous mixing scenario.