✅ Answer: Please pay attention to the following narrations:

1 عَنِ ابْنِ سِنَانٍ يَعْنِي عَبْدَ اللَّهِ قَالَ كَتَبَ أَبِي إِلَى أَبِي عَبْدِ اللَّهِ وَ كَانَ يَقْضِي شَهْرَ رَمَضَانَ- وَ قَالَ إِنِّي أَصْبَحْتُ بِالْغُسْلِ وَ أَصَابَتْنِي جَنَابَةٌ فَلَمْ أَغْتَسِلْ حَتَّى طَلَعَ الْفَجْرُ فَأَجَابَهُ لَا تَصُمْ هَذَا الْيَوْمَ وَ صُمْ غَداً.

📚 Kafi, Vol. 4, p. 105

Translation: Abdullah ibn Sinan was fasting a makeup fast. He wrote a letter to Imam Sadiq (peace be upon him) and said: 'I wake up in the morning while I have to perform ghusl, and janabah has happened to me, and I do not perform ghusl until dawn breaks.' The Imam (peace be upon him) replied: 'Do not fast today (a makeup fast) and fast tomorrow.'

2 عَنْ حَبِيبٍ الْخَثْعَمِيِّ قَالَ: قُلْتُ لِأَبِي عَبْدِ اللَّهِ أَخْبِرْنِي عَنِ التَّطَوُّعِ وَ عَنْ هَذِهِ الثَّلَاثَةِ الْأَيَّامِ إِذَا أَجْنَبْتُ فی أَوَّلِ اللَّيْلِ فَأَعْلَمُ أَنِّي أَجْنَبْتُ فَأَنَامُ مُتَعَمِّداً حَتَّى يَنْفَجِرَ الْفَجْرُ أَصُومُ أَوْ لَا أَصُومُ قَالَ صُمْ.

📚 Faqih, Vol. 2, p. 82

Translation: Habib Khath'ami said: 'I said to Imam Sadiq (peace be upon him): 'Inform me about a recommended fast and (the fasts of) the three days in a month. If I become in a state of janabah at the beginning of the night and I know that I have become in a state of janabah, but I deliberately sleep until dawn breaks, should I fast (the recommended fast) or not?' The Imam said: 'Fast.'

3 عَنِ ابْنِ بُكَيْرٍ عَنْ أَبِي عَبْدِ اللَّهِ قَالَ: سُئِلَ عَنْ رَجُلٍ طَلَعَتْ عَلَيْهِ الشَّمْسُ وَ هُوَ جُنُبٌ ثُمَّ أَرَادَ الصِّيَامَ بَعْدَ مَا اغْتَسَلَ وَ مَضَى مَا مَضَى مِنَ النَّهَارِ قَالَ يَصُومُ إِنْ شَاءَ وَ هُوَ بِالْخِيَارِ إِلَى نِصْفِ النَّهَارِ.

📚 Tahdhib, Vol. 4, p. 322

Translation: Imam Sadiq (peace be upon him) was asked about a person on whom the sun rises while he is in a state of janabah, then after he performs ghusl and part of the day passes, he intends to fast. The Imam said: 'If he wishes, he can fast, and he has a choice until noon (regarding whether to fast or to break the fast).'

4 عَنْ مُحَمَّدِ بْنِ قَيْسٍ عَنْ أَبِي جَعْفَرٍ قَالَ: قَالَ عَلِيٌّ إِذَا لَمْ يَفْرِضِ الرَّجُلُ عَلَى نَفْسِهِ صِيَاماً ثُمَّ ذَكَرَ الصِّيَامَ قَبْلَ أَنْ يَطْعَمَ طَعَاماً أَوْ يَشْرَبَ شَرَاباً وَ لَمْ يُفْطِرْ فَهُوَ بِالْخِيَارِ إِنْ شَاءَ صَامَ وَ إِنْ شَاءَ أَفْطَرَ.

📚 Tahdhib, Vol. 4, p. 187

Translation: Imam Sadiq (peace be upon him) said: 'Ali (peace be upon him) said: 'If a person has not made an intention to fast, and then remembers fasting before he eats food or drinks water, while he has not broken his fast (with anything), then such a person has a choice. If he wishes, he can fast, and if he wishes, he can break his fast.'

✅ From the above narrations, it is clear that a person who wakes up in a state of janabah and has not performed ghusl before dawn breaks cannot fast a makeup fast. However, such a person can fast a supererogatory fast, provided that, according to narration 4, he has not eaten or drunk anything and has not done anything that breaks or invalidates the fast from dawn until the time he intends to fast. Therefore, regarding the question, if his janabah occurred at night, he can intend a supererogatory fast, but if he deliberately became in a state of janabah after dawn, he cannot fast a supererogatory fast either, because intentional janabah breaks the fast, and in hadith 4, the condition for permission to fast a supererogatory fast for such a person is for someone who has not eaten food or drunk water and has not broken his fast with anything.

Remaining in a state of janabah until the adhan of dawn