Euclid Quick Data Release (Q1) XXXVIII. Euclid spectroscopy of quasars. 1. Identification and redshift determination of 3500 bright quasars

The slitless spectroscopy mode of the Near-Infrared Spectrometer and Photometer (NISP) on board the Euclid telescope has enabled e fficient spectroscopy of objects within a large field of view. Nevertheless, the relatively low spectral resolution, overlapping spectra, and contamination pose challenges to source classification and redshift determination using the NISP spectra alone. In this work, we present a large and homogeneous sample of bright quasars identified from the Euclid Quick Data Release (Q1), constructed by combining high-purity candidate selections from Gaia and WISE with the new spectroscopic capabilities of Euclid. Through visual inspection of the Euclid spectra of these quasar candidates, we identify approximately 3500 quasars and determine reliable redshifts in the range of 0 < z less than or similar to 4.8. Of these, 2686 are new spectroscopic identifications relative to existing public compilations. We generated the first Euclid composite spectrum of quasars covering rest-frame near-ultraviolet (NUV) to near-infrared (NIR) wavelengths without telluric lines, which will be pivotal to NIR quasar spectral analysis. We obtained an empirical spectroscopic depth of J(E) less than or similar to 21.5 and H-E less than or similar to 21.3 at the sensitivity of the Wide Field Survey, beyond which the number of securely identified quasars declines sharply. Accordingly, the sample presented in this paper comprises spectroscopically confirmed quasars brighter than these limits. We analysed morphological parameters from the Visible Camera (VIS) using Sersic and model-independent (CAS) metrics, and a deep-learning point spread function fraction ( f(PSF)) to track nuclear dominance. The VIS morphologies show a clear redshift dependence: at low redshift (z < 0.5), obvious host structures are common and a single Sersic model fits about half of the sources; at intermediate redshift (0.5 < z < 2), the nuclear component dominates, with 90% of the Sersic fits saturating at the upper index limit. In this intermediate redshift regime, f(PSF) is available, and we use it as a more reliable compactness measure than the single-Sersic and CAS parameters to quantify nuclear versus host emission. We also explore the novel Euclid NIR colour space and discuss the role of these quasars in refining active galactic nucleus selection techniques for future Euclid data releases.