Praise be to Allah.
The vow must be fulfilled as an act of obedience and righteousness, such as when a person vows to fast one or more days, because the Prophet (peace and blessings of Allaah be upon him) said: “Whoever vows to obey Allaah, let him obey Him.” Narrated by al-Bukhaari (6318).
If the vow mentions a specific time, then it must be fulfilled at that time, such as if a person vows to fast three days at the beginning of the month. But if it is general and not specific, then it is permissible to fast it at any time, except Ramadaan, the days of Eid al-Fitr and Eid al-Adhaa, and the days of al-Tashreeq.
With regard to Ramadaan, the time is already occupied with the obligatory fast, and it is not valid to put any other fast with it. With regard to the days of Eid and al-Tashreeq, it is forbidden to fast on these days. Al-Bukhaari (6212) narrated that Zayd ibn Jubayr said: I was with Ibn ‘Umar, and a man asked him: I vowed to fast every Tuesday or Wednesday as long as I live, but this day coincided with the Day of Sacrifice. He said: Allaah has enjoined fulfilling vows, and He has forbidden us to fast on the Day of Sacrifice. The man repeated (his question), and he gave a similar answer, and no more.
Al-Haafiz Ibn Hajar said: There is consensus that it is not permissible to fast on the day of (Eid) al-Fitr or the day of Sacrifice (Eid al-Adha), whether it is a voluntary fast or in fulfilment of a vow. End quote.
Al-Bukhaari (1998) narrated from ‘Aa’ishah and from Saalim from Ibn ‘Umar (may Allaah be pleased with them all) that they said: No concession was granted allowing us to fast during the days of al-tashreeq, except for the one who cannot find a sacrificial animal.
The scholars drew attention to the fact that it is not permissible to observe any other fast in Ramadaan.
Al-Nawawi (may Allaah have mercy on him) said in al-Majmoo’ (6/315): al-Shaafa’i and his companions (may Allaah have mercy on them) said: Ramadaan is only for the fast of Ramadaan, and it is not valid to observe any other fast at that time. If a resident or a traveller or a sick person intends to fast as an expiation or in fulfillment of a vow or a voluntary fast or a general fast, his intention is not valid and his fast is not valid, and does not count either for what he intended or for Ramadaan. End quote.
Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni: The traveller may not fast in Ramadaan for something other than Ramadaan, such as a vow or making up a fast, because not fasting is permitted to him as a concession to make things easier, and if he does not want to avail himself of that concession, then he has to do what is originally prescribed. If he intends to observe a fast other than Ramadaan, his fast is not valid, either for Ramadaan or for what he intended. This is the correct view, and it is the view of most of the scholars. End quote.
He also said (13/645):
If he vows to Allaah that he will fast for one month, and he intends to fast the month of Ramadaan in fulfilment of his vow, that is not acceptable. Similarly, if he vows to pray two rak’ahs, it is not acceptable for him to pray Fajr in fulfilment of his vow and for Fajr prayer. End quote.
Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: If a person makes a vow that is connected to a condition, he must fulfil the vow when that condition is met and not delay it. For example, if he says: “If Allaah heals me of this disease I will fast for three days for Allaah,” and he recovers from that sickness, then he must hasten to fast and not delay it, because Allaah says (interpretation of the meaning):
“And of them are some who made a covenant with Allaah (saying): ‘If He bestowed on us of His Bounty, we will verily, give Sadaqah (Zakaah and voluntary charity in Allaah’s Cause) and will be certainly among those who are righteous’
76. Then when He gave them of His Bounty, they became niggardly [refused to pay the Sadaqah (Zakaah or voluntary charity)], and turned away, averse.
77. So He punished them by putting hypocrisy into their hearts till the Day whereon they shall meet Him”
As for the vow that is not connected to a condition, such as if a person wants to make himself fast for three days, for no reason, then he must hasten to fulfil it, but it is not like the first case. If Ramadaan comes and he has not fasted, then it is well known that he should start with fasting Ramadaan, and when Ramadaan ends he can fast in fulfilment of his vow. But if he fasts in fulfilment of the vow in Ramadaan, neither his fasting in fulfilment of his vow nor his fasting for Ramadaan are valid.
If a man vows to fast for three days, and he fasts three days of Ramadaan in fulfilment of his vow, what should he do? His fasting did not count in fulfilment of his vow or for Ramadaan. As for it not fulfilling his vow, that is because the time of Ramadaan is restricted to Ramadaan, and he cannot observe any other fast at that time. As for it not counting for Ramadaan, that is because he did not form the intention to fast for Ramadaan, and the Prophet (peace and blessings of Allaah be upon him) said: “Actions are but by intentions, and each man will have but that which he intended.” End quote from al-Liqa’ al-Shahri (52/4).
To sum up: The month of Ramadaan is allocated specifically for the obligatory fast, and it is not permissible to observe any other fast at that time, whether it is a voluntary fast or a fast in fulfilment of a vow, whether one is travelling or not. It is also not permissible to form a combined intention, by intending to observe both the obligatory fast and the fast in fulfilment of a vow at the same time, because they are two separate acts of worship which cannot be done with one intention.
Based on this, it is not permissible for you to fast in fulfilment of a vow with Ramadaan.
And Allaah knows best.