Should she take part in an Islamic contest when she has doubts as to whether her intention is sincerely for the sake of Allah or she simply wants the prize?
Question

I decided to leave a course on Islamic studies, because I was not convinced of the shaykh’s system, but when I wanted to leave, the shaykh announced the prize for the top students. So I decided to stay in the course because I need the money. Could my joining the course be regarded as having been for the purpose of worldly gain and not with the intention of seeking Islamic knowledge for the sake of Allah, may He be exalted? Should I join this course or forget about it, because I am not sure about my intention?
Praise be to Allah.Ruling on accepting prizes for contests in Islamic knowledge
There is nothing wrong with accepting prizes for contests in Islamic knowledge. This has been explained previously in the answer to question no. 156560 .
Secondly:
Sincerity of intention in seeking and acquiring knowledge
What is required of the Muslim, if he enters such contests, is to make his intention sincerely for the sake of Allah, may He be exalted, alone. Therefore his memorisation and study of knowledge should not be for the sake of the prize; rather his aim should be to acquire knowledge and obey Allah, may He be exalted, in that, then the money should come as something secondary to that. Money has a role to play in encouraging people to seek knowledge, but it should not be the aim behind seeking knowledge.
A stern warning has been narrated from the Prophet (blessings and peace of Allah be upon him) concerning the one who seeks Islamic knowledge for worldly purposes. He (blessings and peace of Allah be upon him) said: “Whoever seeks knowledge that should be sought  for the sake of Allah, but he only seeks it for the sake of some worldly gain, will not smell the fragrance of Paradise on the Day of Resurrection.”
Narrated by Abu Dawud (3664) and Ibn Majah (252); classed as sahih by al-Albani in Sahih Abi Dawud.
The scholars of the Permanent Committee for Ifta’ said: There is nothing wrong with awarding cash prizes to motivate students to memorise the Book of Allah, may He be glorified and exalted, but the students should be taught to make their intention sincerely for the sake of Allah when memorising Qur’an, and to regard the prizes as secondary to that; the prizes should not be the aim of memorising.
And Allah is the source of strength. May Allah send blessings and peace upon our Prophet Muhammad and his family and companions.
Shaykh ‘Abdullah ibn Ghadyan, Shaykh ‘Abd ar-Razzaq ‘Afifi, Shaykh ‘Abd al-‘Aziz ibn ‘Abdillah ibn Baz.
From Fatawa al-Lajnah ad-Da’imah – Vol 2 (3/108).
Shaykh ‘Abd al-Karim al-Khudayr (may Allah preserve him) was asked:
What is the ruling on taking part in Qur’an contests with the aim of winning the prizes?
He replied:
Holding contests in memorisation of the Book of Allah and teaching Islamic knowledge, and helping in that, is undoubtedly something that is permitted by the scholars, such as Shaykh al-Islam Ibn Taymiyah and others, by analogy with what has been narrated about [competing in skills required for] jihad.
But the intention should be to acquire knowledge and memorise the Qur’an.
But if the aim and goal is to win the prizes, then undoubtedly this comes under the heading of seeking wealth and worldly gain by means of that which should be sought for the sake of Allah. There is a warning against that and a stern rebuke to those who do that.
Website of Shaykh ‘Abd al-Karim al-Khudayr.
This is similar to what Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) said regarding the one who does Hajj on behalf of someone else in return for payment; his intention should be to show kindness to his brother and perform the rituals and visit the holy places, and he should regard the money as a means of doing that. It should not be the case that his main aim is to obtain the money and he regards Hajj as a means of earning money.
He (may Allah have mercy on him) said in al-Ikhtiyarat (p. 223):
What is recommended for the one who wants to do Hajj on behalf of someone else is to accept money for the purpose of doing Hajj on behalf of someone else, and not do Hajj on behalf of someone else for the purpose of acquiring the money. Whoever wants to show kindness to one who has died, or to see the holy places, may accept money for doing Hajj.
The same applies to any payment that is accepted in return for doing righteous deeds. A differentiation should be made between the one whose aim is to serve religious purposes, for whom the worldly gain is the means of doing that, and the one who does the opposite. What is most likely to be the case is that the one who does the opposite will have no share in the hereafter. End quote.
What we advise you to do is correct your intention, for seeking knowledge is one of the best acts of obedience and worship. Then you can take part in this contest.
If you cannot rid your intention of the aim of seeking money, then there is no point in your taking part in this contest.
And Allah knows best.