Does blood coming out of the nose, and even if small amounts of it enter the throat, break one's fast?

The arrival of blood in the stomach without the fasting person's intention does not break the fast, based on Allah's saying: "Allah does not burden a soul beyond its capacity" (Quran 2:286). However, if one intentionally swallows it, then it breaks the fast. This is evidenced by the prohibition for a fasting person from exaggerating in sniffing water (during ablution) for fear of water reaching the stomach.