We present the first result in exploring the gaseous halo and galaxy correlation using the Dark Energy Spectroscopic Instrument survey validation data in the Cosmic Evolution Survey (COSMOS) and Hyper Suprime-Cam field. We obtain multiphase gaseous halo properties in the circumgalactic medium by using 115 quasar spectra (signal-to-noise ratio > 3). We detect Mg ii absorption at redshift 0.6 < z < 2.5, C iv absorption at 1.6 < z < 3.6, and H i absorption associated with the Mg ii and C iv. By crossmatching the COSMOS2020 catalog, we identify the Mg ii and C iv host galaxies in 10 quasar fields at 0.9< z < 3.1. We find that within the impact parameter of 250 kpc, a tight correlation is seen between the strong Mg ii equivalent width and the host galaxy star formation rate. The covering fraction f c of the strong Mg ii selected galaxies, which is the ratio of the absorbing galaxy in a certain galaxy population, shows significant evolution in the main-sequence galaxies and marginal evolution in all the galaxy populations within 250 kpc at 0.9 < z < 2.2. The f c increase in the main-sequence galaxies likely suggests the coevolution of strong Mg ii absorbing gas and the main-sequence galaxies at the cosmic noon. Furthermore, Mg ii and C iv absorbing gas is detected out of the galaxy virial radius, tentatively indicating the feedback produced by the star formation and/or the environmental effects.