Context. The inner Galaxy is the most complex region of the Milky Way, comprising the early bulge, inner thin and thick discs, and inner halo stars; moreover, the formation of the bar caused transfer of gas and stars from the disc to the inner Galaxy. Moreover, accretion of dwarf galaxies took place along the Galaxy's lifetime, merging with the original bulge. In this work, we sought to constrain the metal-rich stars of the earliest spheroidal bulge. Aims. With the aim of studying the oldest bulge stars, which show a distribution in a spheroid, we applied a selection based on kinematical and dynamical criteria, in the metal-rich range [Fe/H] >-0.8. This analysis complements our previous work on a symmetric sample with [Fe/H] <-0.8. Methods. We derived the individual abundances through spectral synthesis for the elements C, N, O, Al, P, S, K, Mn, and Ce using the stellar physical parameters available for our sample from Data Release 17 of the Apache Point Observatory Galactic Evolution Experiment (APOGEE DR17) project in the H band. We also compared the present results, together with literature data, with chemicalevolution models. Results. The abundances of the alpha elements Mg Si, and Ca, and iron-peak elements V, Cr, Co, and Ni from APOGEE DR17 follow the expected behaviour as compared with the chemical-evolution models. Mn shows the expected secondary behaviour. S and K show a large star-to-star spread, but remain broadly compatible with the model predictions. Phosphorus and cerium display a clear abundance excess around [Fe/H]~ -0.7 that is more pronounced than in our metal-poor sample, suggesting a distinctive chemical signature for the earliest bulge population. Diagnostic diagrams involving [Mg/Mn] versus [Al/Fe] and [Ni/Fe] versus [(C+N)/O] indicate an in situ origin of the bulk of the sample. At super-solar metallicities, a subset of stars shows enhanced K and Mn (and possibly S) together with low [Ce/Fe] ratios, hinting at enrichment processes linked to the nuclear disc and bar. These stars may therefore trace a chemically distinct population shaped by the unique dynamical and star formation conditions of the innermost Galaxy.