Nearly every massive galaxy harbors a supermassive black hole (SMBH) in its nucleus. SMBH masses are millions to billions $M_{\\odot}$, and they correlate with properties of spheroids of their host galaxies. While the SMBH growth channels, mergers and gas accretion, are well established, their origin remains uncertain: they could have either emerged from massive ``seeds\'\' ($10^5-10^6 M_{\\odot}$) formed by direct collapse of gas clouds in the early Universe or from smaller ($100 M_{\\odot}$) black holes, end-products of first stars. The latter channel would leave behind numerous intermediate mass black holes (IMBHs, $10^2-10^5 M_{\\odot}$). Although many IMBH candidates have been identified, none is accepted as definitive, thus their very existence is still debated. Using data mining in wide-field sky surveys and applying dedicated analysis to archival and follow-up optical spectra, we identified a sample of 305 IMBH candidates having masses $3\\times10^4<M_{\\mathrm{BH}}<2\\times10^5 M_{\\odot}$, which reside in galaxy centers and are accreting gas that creates characteristic signatures of a type~I active galactic nucleus (AGN). We confirmed the AGN nature of ten sources (including five previously known objects which validate our method) by detecting the X-ray emission from their accretion discs, thus defining the first \\emph{bona fide} sample of IMBHs in galactic nuclei. The very existence of nuclear IMBHs supports the stellar mass seed scenario of the massive black hole formation.