First of all we would like to congratulate you on this keenness to perform Fajr prayer in the mosque and we ask Allah, may He be glorified and exalted, to make you steadfast and increase you in guidance and righteousness.
The parents should encourage their children -- males and females -- to pray regularly and on time, because the father is the shepherd of his household and is responsible for his flock, and the mother is also a shepherd and is responsible for her flock.
See the answer to question number 103420
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) was asked:
Is it permissible for a man to go out to pray when his children are in the house?
A man is obliged to obey the command of Allah in the verse in which He says (interpretation of the meaning): “O you who believe! Ward off yourselves and your families against a Fire (Hell) whose fuel is men and stones, over which are (appointed) angels stern (and) severe, who disobey not, (from executing) the Commands they receive from Allah, but do that which they are commanded” [al-Tahreem 66:6]. He must tell his family to pray as the Prophet (blessings and peace of Allah be upon him) enjoined when he said: “Tell your children to pray when they are seven years old and smack (lightly) them if they do not do it when they are ten, and separate them in their beds.” And Allah, may He be exalted, tells us that Ismaa’eel, the father of the Arabs (interpretation of the meaning): “used to enjoin on his family and his people As‑Salaah (the prayers) and the Zakaah, and his Lord was pleased with him” [Maryam 19:55].
It is not permissible for him -- the father -- to leave his children sleeping without waking them up to pray and following up on them. It is not sufficient just to wake them up; rather it is essential to follow up, because he may wake them up, then they go back to sleep. End quote.
Fataawa Islamiyyah, 4/215
The Prophet (blessings and peace of Allah be upon him) praised the young man who grows up worshipping Allah. It was narrated from Abu Hurayrah (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: “There are seven whom Allah will shade with His shade on the Day when there will be no shade but His,” a young man who grows up worshipping Allah, and among them he mentioned: “a young man who grows up worshipping his Lord”.
Narrated by al-Bukhaari (629) and Muslim (1031).
One of the most important means of helping a young person to grow up worshipping his Lord is for his parents to take charge of his upbringing and make him get used to that from a young age, and encourage him to do it continually.
Congratulations to the parents for such a son who is upset that his father does not wake him up to offer the Fajr prayer. How many fathers there are who would be prepared to give everything they own in order for their sons to be righteous and adhere to obedience towards Allah. It grieves us that some parents show no interest in encouraging their children to pray on time or to pray in congregation in the mosque.
If your father gets up to pray on time and prays in congregation in the mosque, then the matter is simple, in sha Allah. You can ask him to wake you up to pray and to take you with him, and you can talk to him about the matter calmly.
But if he does not pray and he leaves you sleeping because he feels sorry for you, this is undoubtedly a kind of pity that is inappropriate, and you have to take means of waking up for prayer, such as going to sleep early, setting the alarm clock, making your intention sincere and asking those among your family who wake up to pray to wake you up, or you can request a reminder phone call from some of your friends, and other means that will help you to wake up to pray on time.
It is a good idea to ask the neighbourhood imam to talk about this matter in a special lesson in the mosque or in a Friday khutbah (sermon), so that your father can hear the Islamic ruling about what he is doing and can be alerted to the importance of telling his children and family to pray, and that this is a duty upon him about which he will be asked before Allah, may He be exalted.
We ask Allah, may He be exalted, to increase His bounty and guidance upon you and to open your father's heart to waking you for prayer, and to make you and your family all among those who pray regularly.
And Allah knows best.