Question:
What is the ruling on unintentional swallowing of a little toothpaste while making up for a missed fast, even if that happened during or at the beginning of the Athaan of Fajr?
Answer:
All perfect praise be to Allah, the Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad
is His Slave and Messenger.

If that toothpaste was swallowed unintentionally, whether at the beginning or the end of the day, it would not invalidate fasting, based on the verse (that means): {So fear Allah as much as you are able} [Quran 64: 16]
Ibn Qudaamah
said in his "Al-Mughni", "If the fasting person during Wudoo' (ablution) rinses his mouth or snuffs water into his nostrils, and some of it goes into his/her throat unintentionally and without exaggeration, the fast will still be valid. The same opinion was adopted by Al-Awza'i, Is'haaq and Ash-Shaafi'i in one of his two opinions; and it is also narrated from Ibn ‘Abbaas, may Allah be pleased with him."
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Therefore, the fasting of that person is valid and does not need to be made up.
However, it should be noted that it is impermissible to break a fast that is done to make up for a missed one intentionally and without a valid excuse.
Allah Knows best.