We present homogeneous and accurate iron abundances for almost four dozen (47) of Galactic Cepheids using high-spectral resolution (R$sim$40,000) high signal-to-noise ratio (S/N $ge$ 100) optical spectra collected with UVES at VLT. A significant fraction of the sample (32) is located in the inner disk (RG $le$ 6.9 kpc) and for half of them we provide new iron abundances. Current findings indicate a steady increase in iron abundance when approaching the innermost regions of the thin disk. The metallicity is super-solar and ranges from 0.2 dex for RG $sim$ 6.5 kpc to 0.4 dex for RG $sim$ 5.5 kpc. Moreover, we do not find evidence of correlation between iron abundance and distance from the Galactic plane. We collected similar data available in the literature and ended up with a sample of 420 Cepheids. Current data suggest that the mean metallicity and the metallicity dispersion in the four quadrants of the Galactic disk attain similar values. The first-second quadrants show a more extended metal-poor tail, while the third-fourth quadrants show a more extended metal-rich tail, but the bulk of the sample is at solar iron abundance. Finally, we found a significant difference between the iron abundance of Cepheids located close to the edge of the inner disk ([Fe/H]$sim$0.4) and young stars located either along the Galactic bar or in the nuclear bulge ([Fe/H]$sim$0). Thus suggesting that the above regions have had different chemical enrichment histories. The same outcome applies to the metallicity gradient of the Galactic bulge, since mounting empirical evidence indicates that the mean metallicity increases when moving from the outer to the inner bulge regions.
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