Her father paid her university fees, then the university returned the fees as a prize to her; does her father have the right to take them?

If the matter is as you say, that your father promised to pay
the university fees, then he decided not to ask you to give him the prize
that will be given to you, then it became clear that the prize was no more
than returning the university fees, then this prize belongs to you and what
your father paid previously was a gift with no intention of asking for it
back. This is in addition to the fact that you state that the prize is in
return for future work. 

But we should point out that the father has the right to take
from the wealth of his child – male or female – whatever he needs, without
harming the child, because of the hadeeth of Jaabir ibn ‘Abdillah (may Allah
be pleased with him), according to which a man said: O Messenger of Allah, I
have wealth and a son, and my father wants to take all my wealth. He said,
“You and your wealth belong to your father.” Narrated by Ibn Maajah, 2291;
Ibn Hibbaan in his Saheeh, 2/142, from the hadeeth of Jaabir; Ahmad,
6902 from the hadeeth of ‘Abdullah ibn ‘Amr. 

Ahmad narrated from ‘Amr ibn Shu‘ayb from his father that his
grandfather said: A Bedouin came to the Messenger of Allah (blessings and
peace of Allah be upon him) and said: My father wants to take all of my
wealth. He said: “You and your wealth belong to your father. The best of
what you consume is what you yourself have earned and the wealth of your son
is part of your earnings, so consume it joyfully.” 

It has several isnaads and corroborating evidence that makes
it saheeh. 

See: Fath al-Baari, 5/211; Nasab ar-Raayah,
3/337 

But this is subject to conditions that were laid out by the
scholars: 

1.The father should not be unfair
to the son or harm him, or take anything that he needs.

2.He should not take from the
wealth of one son and give it to another son.

3.The father should be in need of
the wealth; it is not permissible for him to take that which he does not
need, according to the majority of fuqaha’, apart from the Hanbalis, because
of the report narrated by al-Haakim (2/284) and al-Bayhaqi (7/480) from
‘Aa’ishah (may Allah be pleased with her), who said: The Messenger of Allah
(blessings and peace of Allah be upon him) said: “Your children are a gift
from Allah to you, ‘He bestows female (offspring) upon whom He wills, and
bestows male (offspring) upon whom He wills’ [ash-Shoora 42:49], so they
and their wealth belong to you if you need it.” Classed as saheeh by Shaykh
al-Albaani in as-Silsilah as-Saheehah, 2564

Ibn Qudaamah (may Allah have mercy on him) said: The father
may take from his son’s wealth whatever he wants and it becomes his, whether
the father needs what he takes or not, and whether the child is a minor or
an adult, subject to two conditions:

1.That he is not unfair to his
child and does not harm him, and he does not take anything that his son
needs

2.and that he does not take from
the wealth of one son and give it to another.

Abu Haneefah, Maalik and ash-Shaafa‘i said: He does not have
the right to take from the wealth of his son except as much as he needs,
because the Prophet (blessings and peace of Allah be upon him) said: “Your
blood and your wealth are sacred to one another, as sacred as this day of
yours, in this month of yours.” Agreed upon. And it was narrated that the
Prophet (blessings and peace of Allah be upon him) said: “It is not
permissible (to take) the wealth of a Muslim unless he gives it willingly.”
Narrated by ad-Daaraqutni. And because the son has full possession of his
own property, so it is not permissible to take it from him.

End quote from al-Mughni, 5/395 

You stated that your father is not in need; based on that, it
is not permissible for him to take anything from your wealth except with
your consent. 

We appreciate your intention to give the money to your
father, because this comes under the heading of honouring him and treating
him kindly. We ask Allah to compensate you with good.  

And Allah knows best.