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With an unprecedented astrometric and photometric data precision, Gaia EDR3 gives us, for the first time, the opportunity to systematically detect and map in the optical bands, the low mass populations of the star forming regions (SFRs) in the Milky Way. We provide a catalogue of the Gaia EDR3 data (photometry, proper motions and parallaxes) of the young stellar objects (YSOs) identified in the Galactic Plane (|b|<30 deg) within about 1.5 kpc. The catalogue of the SFRs to which they belong is also provided to study the properties of the very young clusters and put them in the context of the Galaxy structure. We applied the machine learning unsupervised clustering algorithm DBSCAN on a sample of Gaia EDR3 data photometrically selected on the region where very young stars (t<10 Myr) are expected to be found, with the aim to identify co-moving and spatially consistent stellar clusters. A subsample of 52 clusters, selected among the 7323 found with DBSCAN, has been used as template data set, to identify very young clusters from the pattern of the observed color-absolute magnitude diagrams through a pattern match process. We find 124440 candidate YSOs clustered in 354 SFRs and stellar clusters younger than 10 Myr and within about 1.5 Kpc. In addition, 65863 low mass members of 322 stellar clusters located within about 500 pc and with ages 10 Myr<t<100 Myr were also found. The selected YSOs are spatially correlated with the well known SFRs. Most of them are associated with well concentrated regions or complex structures of the Galaxy and a substantial number of them have been recognized for the first time. The massive SFRs, such as, for example, Orion, Sco-Cen and Vela, located within 600-700 pc trace a very complex three-dimensional pattern, while the farthest ones seem to follow a more regular pattern along the Galactic Plane.