The results of three different searches for neutrino candidates, associated with the IceCube-170922A event or from the direction of TXS 0506+056, by the ANTARES neutrino telescope are presented. The first search refers to the online follow-up of the IceCube alert; the second is based on the standard time-integrated method employed by the Collaboration to search for point-like neutrino sources; the third uses the information from the IceCube time-dependent analysis reporting a bursting activity centered on December 13, 2014, as input for an ANTARES time-dependent analysis. The online follow-up and the time-dependent analysis yield no events related to the source. The time-integrated study performed over a period from 2007 to 2017 fits 1.03 signal events, which corresponds to a p-value of 3.4% (not considering trial factors). Only for two other astrophysical objects in our candidate list, a smaller p-value had been found. When considering that 107 sources have been investigated, the post-trial p-value for TXS 0506+056 corresponds to 87%.