We present the discovery of three super-Earth candidates orbiting HD 48948, a bright K-dwarf star with an apparent magnitude of $m_V$ = 8.58 mag. As part of the HARPS-N Rocky Planet Search programme, we collect 189 high-precision radial velocity measurements using the HARPS-N spectrograph from 2013 October 6, to 2023 April 16. Various methodologies are applied to extract the radial velocities from the spectra, and we conduct a comprehensive comparative analysis of the outcomes obtained through these diverse extraction techniques. To ensure the robustness of our findings, we employ several methods to address stellar variability, with a focus on Gaussian Process regression. To account for the impact of stellar variability and correlated noise in the radial velocity data set, we include activity indicators, such as $\log R^{^{\prime }}_{\mathrm{HK}}$ and bisector span, in the multidimensional Gaussian Process regression. Our analysis reveals three planetary candidates with orbital periods of 7.3, 38, and 151 d, and minimum masses estimated at $4.88 \pm 0.21$ M$_{\oplus }$, $7.27 \pm 0.70$ M$_{\oplus }$, and $10.59 \pm 1.00$ M$_{\oplus }$, respectively. The outermost planet resides within the (temperate) habitable zone, positioned at a projected distance of $0.029\,{\rm arcsec}$ from its star. Given the close proximity of this planetary system, situated at a distance of 16.8 parsecs, HD 48498 emerges as a promising target (closest super-Earth around FGK stars) for future high-contrast direct imaging and high-resolution spectroscopic studies.