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Cosmic Chance Superpositions: Largest Catalog of Quasar-Galaxy Pairs at a Projected Separation of $D \lesssim 20$ kpc

We present the largest catalogue to date of Galaxies On Top Of Quasars (GOTOQs), systems where the sightline to a background quasar passes directly through or very close to a foreground galaxy. Using $\approx$1.1 million quasar spectra from SDSS DR16 and the DESI Early Data Release, we identify 1345 unique GOTOQs over the redshift range $0.0045 \leq z \leq 1.09$, more than quadrupling the number previously known. The catalogue combines both absorption agnostic and absorption selected searches, enabling a statistically robust characterization of gas in galaxies at projected separations $D \lesssim 20$ kpc. The GOTOQ emission line ratios indicate that their host galaxies are predominantly normal, star forming disks with typical dust extinctions of $A_V \approx 0.5$ mag. We measure the MgII covering fraction at $D \lesssim 20$ kpc and find it to be remarkably high, $f_c = 98.2^{+1.3}_{-4.5}$ per cent, indicating that these systems trace gas rich, metal enriched regions at the disk halo interface. The median colour excess towards the quasar line of sight, $E(B-V) = 0.087$, is significantly higher than that of typical MgII absorbers, underscoring the dust rich nature of GOTOQ sightlines. From a high signal to noise composite spectrum, we report the first statistical detection of the diffuse interstellar band at $λ4428$ ($W_r = 0.055 \pm 0.011$ angstrom), revealing the presence of complex organic molecules at the disk halo interface. This catalogue provides a powerful reference sample for future multi wavelength studies of gas flows, cold gas, and dust evolution in the inner circumgalactic medium.