ANTARES and Baikal-GVD are both Cherenkov neutrino telescopes located in the Northern Hemisphere so their fields of view almost overlap allowing for a combined study of the sky. ANTARES sends alerts after a fast online analysis based on energy and reconstruction direction of track-like events. From December of 2018 until the beginning of 2021, Baikal-GVD received 38 ANTARES alerts, and followed up 32. No coincidence was found. However, a search of the Baikal-GVD cascade sample showed some events falling within an angular distance of less than 5° for three of the ANTARES alerts in a time span of 48 hours. A dedicated offline analysis based on the full ANTARES data sample has been started to search for additional coincident tracks and cascades at a 3σ significance. In this work we present the final results of the offline analysis of the three ANTARES alerts: limits on the astrophysical neutrino fluence are reported.