We report the serendipitous discovery of three new open clusters, named UFMG 1, UFMG 2 and UFMG 3 in the field of the intermediate-age cluster NGC 5999, by using Gaia DR2 data. A colour-magnitude filter tailored for a proper selection of main-sequence stars and red clump giants turned evident the presence of NGC 5999 and these three new stellar groups in proper motion space. Their structural parameters were derived from King-profile fittings over their projected stellar distributions and isochrone fits were performed on the clusters cleaned colour-magnitude diagrams built with Gaia bands to derive their astrophysical parameters. The clusters projected sky motion were calculated for each target using our members selection. Distances to the clusters were inferred from stellar parallaxes through a bayesian model, showing that they are marginally consistent with their isochronal distances , considering the random and systematic uncertainties involved. The new clusters are located in the nearby Sagittarius arm (d~1.5kpc) with NGC 5999 at the background (d~1.8kpc). They contain at least a few hundred stars of nearly solar metallicity and have ages between 100 and 1400Myr.