The Shulhan Aruch (O.H. 291:1) writes that one should be exceedingly careful to fulfil the Mitzvah of Seuda Shelishit. If one still feels full from the previous meal, one can fulfil the obligation by eating only a Kabetza of bread, but if one feels that one cannot eat at all, one need not trouble oneself to eat. Nevertheless, one should ideally try to plan ahead such that one have an appetite for Seuda Shelishit.
The HIDA (Mahzik Beracha) writes that a person’s day typically consists of meals, one in the morning and one at night. Thus, unlike the first two meals of Shabbat, which are habitual meals that one would eat regardless of the day, Seuda Shelishit is an extra meal and therefore by eating it, it shows a higher level of honor towards Shabbat.
According to Kabbalah, each of the three Shabbat meals corresponds to one of the Avot and Seuda Shelishit corresponds to Ya’akov Avinu and one should have him in mind while eating this meal. Furthermore, the Arizal (Peri Etz Haim) explains that Seuda Shelishit has the power to save one from the war of Gog and Magog and from the judgment of Gehinom.
The Rama (ibid:2) writes that one should not drink water between Minha of Shabbat and Arvit since, on a Kabbalistic level, the souls return to Gehinom. As such, he does not recommend that Seuda Shelishit be eaten at all in between Minha and Arvit, but rather before Minha. The Arizal qualifies the ruling of the Rama by saying that water should not be consumed before reciting Havdala, but that it is permissible to do so during the course of Seuda Shelishit, even if it stretches into Ben Hashemashot.Indeed, the Kaf Hahaim (ibid:17) writes that he was never particular about avoiding water at the time of Seuda Shelishit. Furthermore, Rabbi Yehuda Ayash (ibid:4) writes that the Shulhan Aruch itself does not mention this Halacha and that in the majority of Sephardic lands, Seuda Shelishit takes place between Minha and Arvit and that water may be consumed at this time as well.
Summary: Seuda Shelishit takes place between Minha of Shabbat and Arvit of Motzae Shabbat.