Praise be to Allah.

Shaykh Muhammad ibn ‘Uthaymeen (may Allah have mercy on him) was asked this question and he said: 

Calling people to Allah (d’awah) is a communal obligation (fard kifayah); if sufficient people undertake to do it, the rest are then absolved of the obligation. If a person finds that he has to do it and no one else can take his place, then it takes priority over reading Quran over one who is affected by the jinn. That is because the results of d’awah are certain whereas the results of reading Quran over one who is affected by the jinn may not be certain. How many people have had Quran recited over them and have not benefited. 

So if this man realizes that he has to do d’awah and no one else can take his place, then he must do d’awah even if it means he does not recite Quran over one who is affected by the jinn. 

But if it is the matter of fard kifayah, then you should look and decide what is in people’s best interests. If it is possible to combine the two – which seems to be the case – by devoting a day for one and a day for the other whilst continuing to engage in d’awah, that is better, so that he may benefit his Muslim brothers who are suffering from this affliction and so that the work of calling people to Allah may continue at the same time. 

With regard to the correct treatment of those who are affected by the jinn, this varies from one case to another, but the best is to recite Quran over the person, such as the words (interpretation of the meaning): 

“O assembly of jinn and men! If you have power to pass beyond the zones of the heavens and the earth, then pass beyond (them)! But you will never be able to pass them, except with authority (from Allah)!

Then which of the Blessings of your Lord will you both (jinn and men) deny?

There will be sent against you both, smokeless flames of fire and (molten) brass, and you will not be able to defend yourselves.

Then which of the Blessings of your Lord will you both (jinn and men) deny?”
[55:33-36] 

Because this reminds them [the jinn] that they cannot flee from Allah. You should also recite al-Mu’awwadhatayn [the last two Surahs of the Quran] and Qul Huwa Allahu Ahad [112] and ayat al-Kursiy [2:255]. You may also preach to them as Shaykh al-Islam Ibn Taymiyah used to do, telling them, “It is haram for you to harm the Muslims or to beat them,” etc. 

With regard to accepting payment for this: if he does not take money it is better, but if he takes it without stipulating payment beforehand that is acceptable. If those for whom he is reading do not carry out their duties towards the reader and he insists that he will only read for them if he is given something in return, there is nothing wrong with that, as this is what the people of the raiding party sent out by the Prophet (peace and blessings of Allah be upon him) did. It was narrated that Abu Sa’eed (may Allah be pleased with him) said: “A group of the companions of the Prophet (peace and blessings of Allah be upon him) set out on a journey and traveled until they stopped in (the land of) one of the Arab tribes. They asked them for hospitality but they refused to welcome them. The chief of this tribe was stung by a scorpion and they tried everything but nothing helped them. Some of them said, ‘Why don’t you go to those people who are camped (near us), maybe you will find something with them.’ So they went to them and said, ‘O people, our chief has been stung by a scorpion and we have tried everything but nothing helped him. Can any of you do anything?’ One of them said, ‘Yes, by Allah, I will recite ruqyah (incantation) for him, but by Allah we asked you for hospitality and you did not welcome us, so I will not recite ruqyah for you until you give us something in return.’ Then they agreed upon a flock of sheep. Then he went and spat drily and recited over him Al-hamdu Lillahi Rabb il-‘alameen [Surat al-Fatihah]. (The chief) got up as if he was released from a chain and started walking, and there were no signs of sickness on him. They paid them what they agreed to pay. Some of them (i.e. the companions) then suggested to divide their earnings among themselves, but the one who performed the ruqyah said, ‘Do not divide them until we go to the Prophet (peace and blessings of Allah be upon him) and tell him what happened, then wait and see what he tells us to do.’ So they went to the Messenger of Allah (peace and blessings of Allah be upon him) and told him what had happened. The Messenger of Allah (peace and blessings of Allah be upon him) asked, ‘How did you know that it (al-Fatihah) is a ruqyah?’ Then he added, ‘You have done the right thing. Share out (the flock of sheep) and give me a share too.’ And the Messenger of Allah (peace and blessings of Allah be upon him) smiled.”  (al-Bukhari, Muslim).