ESPRESSO is the VLT ultra-stable high-resolution spectrograph, developed by institutions from Switzerland, Italy, Portugal, Spain, and ESO, located in the combined Coudé Lab of the VLT at ESO, and is able to operate either using one 8.2m-VLT UT or simultaneously with the four VLT UTs. ESPRESSO started routine operations in October 2018 at ESO, and is designed to achieve a radial velocity precision of 10 cm/s, thus opening the possibility to explore new frontiers in science such as the search for rocky planets (Pepe et al. 2021).ESPRESSO has demonstrated unprecedented capabilities, being so far very successful in detecting and characterizing low-mass Earth-like and sub-Earth-like planets. ESPRESSO has exploited its sub-m/s capabilities to break the Earth-mass barrier, thus providing a unique ground-based facility with great synergy with exoplanet dedicated satellites, such as Kepler (e.g. Toledo Padrón et al. 2020; Mortier et al. 2020), TESS (e.g. Demangeon et al. 2021; Barros et al. 2022; Lavie et al. 2023) and CHEOPS (e.g. Leleu et al. 2021).ESPRESSO has confirmed the Earth-mass planet Proxima b and discovered the sub-Earth mass planet Proxima d with 0.26 Earth masses, just about twice the Mars mass, from the measurement of a tiny RV semiamplitude velocity of 39 cm/s together with a simultaneous precise characterization of the activity of the star (Suárez Mascareño et al. 2020; Faria et al. 2022). We have recently reported the discovery of two Earth-mass planets in the habitable zone for the nearby relatively faint M dwarf star GJ1002 (Suárez Mascareño et al. 2023). All these results further stimulate the search for Earth and sub-Earth mass planets in the nearest stars of the solar neighbourhood, and encourage new detail studies with current and future facilities such as ANDES@ELT (Marconi et al. 2022; Pallé et al. 2023).The Barnard's star (GJ 699) is the second closest stellar system to the Sun, after the alpha Centauri stellar system, at a distance of about 1.8 parsecs. The isolated star GJ 699 is a low-magnetic activity M4V star that offers a unique opportunity to search for Earth like planets within its habitable zone. The Barnard's star is considered a primary target within the ESPRESSO Guaranteed Time Observations (GTO) due to its proximity to our Sun. Here we present ESPRESSO GTO observations of the Barnard's star focusing on revealing and discussing planet candidates.