Should he interrupt his prayer in order to answer one of his parents if they call him?

If a Muslim is offering an obligatory prayer, he should not
interrupt it in order to answer the call of his father or mother. But he
can alert the one who is calling him to let him know that he is busy with
the prayer, either by saying tasbeeh (“Subhaan Allah”) or by raising his
voice in recitation and the like. 

And it is prescribed for him to make the prayer brief, then
when he has finished he can answer the call. 

Al-Bukhaari (707) narrated from Abu Qataadah (may Allah be
pleased with him) that the Prophet (blessings and peace of Allah be upon
him) said: “Sometimes I stand in prayer, intending to make it lengthy, then
I hear a child crying, so I make my prayer brief because I do not want to
cause hardship to his mother.” 

This indicates that it is prescribed to make the prayer brief
if there is something that is distracting the worshipper. 

If it is a naafil prayer, if he knows that his father or
mother will not object to him completing the prayer, he may complete it and
then answer them once he is free. But if he knows that they will object to
him completing the prayer he may interrupt his prayer and answer them, and
there will be no blame on him for that. Then he can go back and start
praying again. 

Al-Bukhaari (3436) and Muslim (2550) narrated from Abu
Hurayrah (may Allah be pleased with him) that the Prophet (blessings and
peace of Allah be upon him) said: “Jurayj used to worship in his cell, and
his mother came to him. She said: ‘O Jurayj! I am your mother, speak to me.’
She found him praying and he said: ‘O Allaah, my mother or my prayer?’ And
he chose his prayer. She went away, then she came back a second time and
said: ‘O Jurayj! I am your mother, speak to me.’ He said: ‘O Allaah, my
mother or my prayer?’ And he chose his prayer. She said: ‘O Allaah, this is
Jurayj and he is my son, and I spoke to him but he refused to speak to me. O
Allaah, do not let him die until he has seen prostitutes.’” He said: “If she
had prayed that he be tempted, he would have fallen prey to temptation.” 

Al-Nawawi gave this report the title: Honouring one’s parents
takes precedence over voluntary prayer and other actions. 

Al-Nawawi (may Allah have mercy on him) said: 

The scholars said: What would have been correct in this case
is answering her, because he was offering a naafil prayer and continuing
with it is voluntary and not obligatory, whereas answering one’s mother and
honouring her is obligatory, and disobeying her is haraam. He could have
shortened his prayer and answered her, then gone back to his prayer… End
quote. 

See: Fath al-Baari by al-Haafiz Ibn Hajar (may Allah
have mercy on him), al-Mawsoo‘ah al-Fiqhiyyah, 20/342 

It says in al-Durr al-Mukhtaar (2/54) – which is a
Hanafi book: 

If either of his parents calls him during an obligatory
prayer, he should not answer unless his parent is urging him to come and
help. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said: 

If your parents call you when you are praying, it is
obligatory to answer them, on condition that the prayer is not an obligatory
one. If it is an obligatory prayer, it is not permissible to answer them,
but if it is a naafil prayer, you should answer them. 

But if they are people who give things their due measure and
if, when they realise that you are praying, they will excuse you, then in
this case you should indicate to them that you are praying – either by
clearing your throat or saying “Subhaan Allah” or raising your voice in the
verse or du‘aa’ you are reciting – so that the one who is calling will
realise that you are praying. 

But if they are otherwise, and they are people who will not
make excuses or who want an immediate response, then you should interrupt
your prayer and speak to them. 

But in the case of an obligatory prayer, you should not
interrupt it for anyone except in the case of necessity, such as if you see
someone who you fear will fall into mortal danger, such as falling into a
well or into the sea or into a fire. In that case, you should interrupt your
prayer because it is a case of necessity. Otherwise, it is not permissible
to interrupt an obligatory prayer. End quote. 

Sharh Riyaad al-Saaliheen, p.
302 

And Allah knows best. 

See also the answer to question no.
65682.