Praise be to Allah.
Obedience to parents is obligatory upon the child with regard to that which will benefit them and will not cause him any harm. But if there is no benefit for them in it, or it will harm the child, then he is not obliged to obey them in that case.
Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said in al-Ikhtiyaaraat (p. 114): The individual is obliged to obey his parents so long as it does not involve any sin, even if they are evildoers… This applies to that which is beneficial for them and is not harmful for him. End quote.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
If they say to him: Do not eat this food, do not eat meat, do not eat rice, do not eat a certain thing – and it is something that he wants to eat – then he is not obliged to obey them in that, because it does not serve any interest for them, and it is harmful for him because it causes him to miss out on something that he likes.
End quote from Liqa’ al-Baab al-Maftooh (49/6)
This is the guideline with regard to what is required of the child in terms of obedience to his parents.
Based on that:
If your staying up at night is detrimental to your parents’ interests, because it will lead to you sleeping for a long time during the day, which will prevent you from doing what they ask of you, then in that case it is obligatory for you to obey them.
But if you can take care of their interests and serve them, and not fall short in that, then what appears to be the case is that you are not obliged to obey them with regard to not staying up at night.
If you are not able to get up to pray Fajr except by staying up all night in the summer, then there is no blame on you if you stay up at night for something that is of benefit to you, and thus be able to pray Fajr on time.
In this case you should try to win your parents’ approval, and explain to them that you are only doing that because you are keen to pray Fajr on time.
Whatever the case, what you must do is strive to offer the prayer on time, for prayer is the best and noblest of deeds, and one of the greatest of prayers is Fajr prayer.
But you should try to look for other alternatives so that you do not have to stay up all night, such as using an alarm clock or phone, or asking one of your friends to call you to wake you up, or perhaps your parents can help you and wake you up, and other solutions which will combine the interests of praying on time and pleasing your parents with other interests that will benefit you, namely sleeping at night, which is more beneficial and healthy than sleeping during the day, because staying up at night has an impact on a person’s health and energy in general terms.
And Allah knows best.