Will getting married to someone who is possessed affect the children in the future?

Firstly: 

The fact that a jinni can possess a human and enter his body and cause seizures is proven according to the Qur’an and Sunnah and scholarly consensus. 

But no such thing can happen except by Allah’s leave. 

Secondly: 

Being possessed by a jinni and having seizures as a result is not an impediment to marriage, but the one who is affected by that must inform a prospective spouse of it, because having these seizures is a defect which should be disclosed as it has an impact on some of the basic aims of marriage. 

See also the answers to questions no. 135785 and 158489

Thirdly: 

Such situations may have an impact on the marriage as the husband may not have the patience to put up with this problem that affects his wife, and that may lead him to dislike interacting with her, so he will not treat her kindly or interact with her in a reasonable manner as enjoined by Allah. 

But with regard to the impact of the jinni that is possessing her on the marriage and on married life, that impact will be affected by the degree of their faith and patience. If a person’s faith is strong, the Shaytaan will have no way to affect them, as Allah, may He be glorified and exalted, says (interpretation of the meaning):

“Verily! He has no power over those who believe and put their trust only in their Lord (Allah).

His power is only over those who obey and follow him (Satan), and those who join partners with Him (Allah) (i.e. those who are Mushrikoon – polytheists)”

[an-Nahl 16:99-100]. 

And Allah, may He be exalted, says (interpretation of the meaning):

“ ‘And Istafziz (literally means: befool them gradually) those whom you can among them with your voice (i.e. songs, music, and any other call for Allahs disobedience), make assaults on them with your cavalry and your infantry, mutually share with them wealth and children (by tempting them to earn money by illegal ways usury, etc., or by committing illegal sexual intercourse, etc.), and make promises to them.” But Satan promises them nothing but deceit.

‘Verily! My slaves (i.e the true believers of Islamic Monotheism), you have no authority over them. And All-Sufficient is your Lord as a Guardian’”

[al-Isra’ 17:64, 65]. 

But if a person’s faith is weak, the Shaytaan will toy with him as children play with a ball. 

Fourthly: 

The possession and what may result from it of seizures is a test for which Allah will reward the one who is tested with it, so patience will bring the greatest reward. 

Al-Bukhaari (5652) and Muslim (2576) narrated that ‘Ata’ ibn Abi Rabaah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: Ibn ‘Abbaas said to me: Shall I show you a woman of the people of Paradise? I said: Yes. He said: This black woman came to the Prophet (blessings and peace of Allah be upon him) and said: I have epilepsy and I become uncovered. Pray to Allah for me. He said: “If you wish, you may be patient, and Paradise will be yours, or if you wish, I will pray to Allah to heal you.” She said: I will be patient. She said: But I become uncovered; pray to Allah that I will not become uncovered. So he prayed for her. 

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

This indicates that the one who suffers from seizures will be granted the highest reward for it. End quote from Sharh Muslim (132/16) 

Ibn Hajar (may Allah have mercy on him) said:

Al-Bazzaar narrated a similar story from Ibn ‘Abbaas with a different isnaad, according to which she said: “I am afraid that the evil one may cause me to become uncovered.” It may be understood from some of the different versions of the hadeeth that what she was suffering from was the kind of seizures caused by the jinn and not that which results from dysfunction in the brain.”

End quote from Fath al-Baari (115/10) 

Fifthly: 

It is possible to treat this woman and expel the jinni from her, by Allah’s leave and by His strength and power, may He be glorified, for the Shaytaan is weak and he has no power over any believer, man or woman; rather it is harm that Allah may decree for whomever He will among His slaves, and for the believing men and women it is mercy and expiation, and will raise them in status. 

The best means of treating this problem is to recite Qur’an over the one who is afflicted and to perform ruqyah by reciting the du‘aa’s that have been narrated (from the Prophet (blessings and peace of Allah be upon him)), and regularly reciting the prescribed wird and dhikr from the Qur’an, and that will disappear, by Allah’s leave. 

Al-Haafiz said: 

The hadeeth indicates that treating all diseases with du‘aa’ and turning to Allah is more beneficial and more efficacious than treating them with medications, because the effect of that is greater than the effect of physical medicine. But it is only efficacious in two cases: (i) if the sick person is sincere and (ii) if the one who treats him is strong in terms of piety and putting his trust in Allah.

End quote from Fath al-Baari (115/10). 

See the answer to question no. 1819 and 105336

Sixthly: 

What we advise you to do is not to be hasty with regard to this marriage. Look at your own situation and that of the girl; if you think it most likely that you can put up with this situation, and that you will be patient with her, especially after having found out about her situation from those who know her or who have treated her, and the girl is good in terms of religious commitment and character, then put your trust in Allah and propose to her, especially since you have ties of kinship with her and it is more appropriate that you should care for her and be patient with her, in  sha Allah,. 

But if you know that you will not be able to bear it with patience, and it might be difficult for you to have a lasting relationship with her, then it is better not to get involved in this marriage, and there is no need for you to open the door to something that you might not be able to bear, or to shut that door again. 

See also the answer to question no. 158489

And Allah knows best.