Mistakenly Blessed During Yahrzeit Fast, Can He Eat?

What should someone do if they are accustomed to fasting on the anniversary of their father's death and mistakenly blessed food?

He should eat less than a kezayit, and the fast will be considered fulfilled.

Written in the book Birkei Yosef, Orach Chaim, Siman 568: "Someone who is in a fast and forgot, took the food and blessed it, and then remembered the fast, should eat less than a kezayit because of the blessing, and the fast will be considered fulfilled. My teacher, the Rabbi, in his book Nachpeh Bakesef, Orach Chaim, Siman 6. And Rabbi Admat Kodesh, part 1, Orach Chaim (Siman 13) doubted this. But his words do not seem correct. And I found in the responses of Rabbi Mahara"r Shabtai Garmizan, manuscript of the elders in the holy city of Jerusalem, that he was asked about this, and he answered like my teacher, the Rabbi, of blessed memory." (And in Shaarei Teshuva it implies that in the four fasts it is forbidden to eat, and he should say "immediately" as soon as he remembers.) And although in other fasts this is not ruled, in the yahrzeit fast, which is a light fast, the opinion of our teacher, the Rabbi, shlita, is that he should eat less than a kezayit.