Praise be to Allah.
The Prophetic Sunnah indicates that anything that reaches the stomach via the nose spoils the fast. We see this in the words of the Prophet (blessings and peace of Allah be upon him) to the one who is doing wudoo’: “Exaggerate in your istinshaaq (taking water into the nose), unless you are fasting.” Narrated by at-Tirmidhi (631) and Abu Dawood (142); classed as saheeh by al-Albaani in Saheeh Sunan at-Tirmidhi.
Shaykh Muhammad ibn ‘Uthaymeen (may Allah have mercy on him) said:
This indicates that the fasting person should not exaggerate in istinshaaq, and we do not know of any reason for that except the fact that exaggerating therein may cause water to reach the stomach, which would spoil the fast. Based on that, we say that everything that reaches the stomach via the nose or mouth breaks the fast.
End quote from ash-Sharh al-Mumti‘ (6/367-368).
But this applies to the one who puts something into his nose deliberately, knowing that it will reach the stomach, and does that during the day.
But if he does that at night, then it reaches his stomach during the day, his fast is still valid and he does not have to do anything.
This was stated clearly by some of the fuqaha’.
Others stated that if he applies kohl to his eyes at night, then the kohl reaches his throat during the day, he does not have to do anything, so the same applies to that which is applied in the nose.
It says in Haashiyat as-Saawi (1/699):
If he applies kohl at night, or puts something in his ear or nose, or applies oil to his head at night, then some of that comes down to his throat during the day, he does not have to do anything.
See also Sharh Mukhtasar Khaleel by al-Kharashi (2/248).
If he has intercourse at night, then emits maniy after Fajr, what appears to be the case is that he does not have to do anything, as in the case of one who applies kohl at night, then it comes down (to his throat) during the day. End quote.
Al-Qarraafi stated in adh-Dhakheerah (2/506) that whoever applies kohl at night, it will not matter if the kohl comes down to his throat during the day.
Ibn Muflih al-Hanbali said in al-Furoo‘ (5/15):
If a fasting person has a wet dream or emits maniy as a result of intercourse that occurred at night, that does not break the fast, and there is agreement on that [i.e., among the three imams, Abu Haneefah, Maalik and ash-Shaafa‘i]. The apparent meaning is: Even if a man has intercourse near the time of Fajr. The case of one who applies kohl at that time may be likened to this.
End quote from al-Majmoo‘ (6/348)
An-Nawawi said, commenting on that: That is because that (emission of maniy) was a result permissible intimacy (i.e., before the fast began), therefore he does not have to do anything.
Ibn Qaasim said in Haashiyat ar-Rawd al-Murbi‘ (3/390):
If he applies kohl at night and notices it in his throat during the day, that does not break the fast, because the thing that led to that was not done during the day. End quote.
Shaykh Muhammad Mukhtaar ash-Shinqeeti said in Sharh az-Zaad (4/99):
If he applies kohl at night and notices the taste thereof during the day, that does not break the fast, because he applied it during the night, and the time when it reached the throat does not matter, because refraining from anything that may break the fast, which the accountable person is commanded to do, has been fulfilled, and because the real meaning of fasting is refraining from that which breaks the fast. End quote.
For more information, please see the answer to question no. 49721.
And Allah knows best.