His father does not let him pray Fajr in the mosque – should he obey him?

Firstly: 

To begin with, we would like to congratulate you for these
good intentions and keenness to offer the obligatory prayers in
congregation. We ask Allaah to make you steadfast in adhering to Islam and
righteousness, and we pray that your father’s actions will not put you off
from doing what is right and following true guidance. Before answering your
question, we should mention a very important matter, which is:  

Honouring and obeying one’s parents has been enjoined by
Allaah in many places in His holy Book, such as the verses in which He says
(interpretation of the meaning): 

“Worship Allaah and join none with Him (in worship); and
do good to parents …”

[al-Nisa’ 4:36] 

“And your Lord has decreed that you worship none but Him.
And that you be dutiful to your parents. If one of them or both of them
attain old age in your life, say not to them a word of disrespect, nor shout
at them but address them in terms of honour.

24. And lower unto them
the wing of submission and humility through mercy, and say: ‘My Lord! Bestow
on them Your Mercy as they did bring me up when I was young’”

[al-Isra’ 17:23, 24]

Obedience to parents is obligatory, unless they tell you to
disobey Allaah, in which case you are not obliged to obey them, because the
Prophet (peace and blessings of Allaah be upon him) said: “There is no
obedience if it involves disobedience towards Allaah, rather obedience is
only in matters that are right and proper.” Narrated by al-Bukhaari, 6830;
Muslim, 1840. 

With regard to prayer in congregation, this is obligatory,
and it is not permissible for a father to forbid his son who has reached the
age of maturity to do it. Rather parents should enjoin their sons to pray in
congregation and encourage and urge them to do so. If the father notices
that his son is falling short in that regard, then he must make him aware of
his responsibilities and remind him that he will be questioned about it
before Allaah on the Day of Reckoning. So he should enjoin what is right and
forbid what is wrong, and remind those who are under his care of their
duties towards their Lord and the seriousness of neglecting those duties.  

If the father falls short in his duties towards his children
by not enjoining what is good and forbidding what is evil, or encouraging
them to do good and warning them against evil, this does not absolve them
(the sons) of sin if they fall short in their duties or commit haraam
actions. 

If the father forbids his sons to perform a duty that has
been enjoined upon them by Allaah, in that case they do not have to obey him
by disobeying Allaah or by forsaking that which Allaah has commanded. If the
father tells his son not to offer all or some of the prayers in
congregation, then he has told him to commit a sin, and this case he is not
to be obeyed, but at the same time he should be treated with kindness and
respect. 

With regard to your question about going secretly to pray
Fajr, this is good on your part, but it is treating your father badly
without realizing it. You father is committing a sin so long as he forbids
you to pray in congregation, and even if you go out secretly, the burden of
sin is not lifted from him, because he is still telling you to do something
wrong and forbidding you to do something good, even if you go out to pray
without his knowledge. So you have to try to convince him of the Islamic
ruling, even if you get someone else to do it, if he will not listen to you
or he thinks you are too young. If he does not respond, then there is no sin
on you if you go out without his permission or knowledge, but you have to be
very careful when going to the mosque.

Secondly: 

We say to your father – may Allaah guide him – that Allaah
has given you a great responsibility, which is to teach and advise your
family, including your wife and children. The Messenger (peace and
blessings of Allaah be upon him) said in a hadeeth whose authenticity is
agreed upon: “Each of you is a shepherd and responsible for his flock. The
man is the shepherd of his family and is responsible for his flock.” 

Allaah has commanded you to protect yourself and your family
from His Fire, as 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 Allaah, but do that which they are commanded”

[al-Tahreem 66:6]

And He says, enjoining the prayer (interpretation of the
meaning): 

“And enjoin As‑Salaah (the prayer) on your family, and be
patient in offering them [i.e. the Salaah (prayers)]. We ask not of you a
provision (i.e. to give Us something: money): We provide for you. And the
good end (i.e. Paradise) is for the Muttaqoon (the pious)”

[Ta-Ha 20:132]

Ibn al-Qayyim (may Allaah have mercy on him) said: 

Whoever neglects to
teach his son that which will benefit him, and ignores him, has done
something very bad indeed. Most children go astray because of their parents
who neglect them and fail to teach them the duties and Sunnahs of their
religion. They neglect them when they are young so they do not benefit
themselves or benefit their parents when they grow up. End quote. 

Tuhfat al-Mawdood, p. 229 

We ask you an important question: Where are you when it is
time for Fajr prayer? Is it not obligatory for you to offer the prayer in
congregation? Is it not obligatory for you to be a good example for your
family and children by praying in congregation in the house of Allaah? If
you do that, you will have fulfilled the duty that Allaah has enjoined upon
you, and you will have helped your son to pray in the mosque, and you will
put your mind at rest if you are worried about him going alone.

Remember that the Prophet (peace and blessings of Allaah
be upon him) has told us that whoever prays Fajr in the mosque will be under
the protection of Allaah, so how can you fear for one who is under the
protection of Allaah, may He be exalted? 

It was narrated that Jundub ibn ‘Abd-Allaah (may Allaah be
pleased with him) said: The Messenger of Allaah (peace and blessings of
Allaah be upon him) said: “Whoever prays Fajr is under the protection of
Allaah, so do not fall short with regard to the rights of Allaah, for anyone
who does that, Allaah will seize him and will throw him on his face into the
Fire of Hell.”Narrated by Muslim, 657. 

We ask Allaah to help you to fulfil the trust and to make you
a good example for your family, and to make you help your son to offer the
prayers in the house of Allaah. 

And Allaah knows best.