She is possessed and the jinni speaks on her lips and refuses to leave her

Firstly: 

We ask Allaah to take away from your cousin what she is
experiencing and to heal her, and divert that jinni away from her, for He is
All Hearing and Ever Responsive. 

Secondly: 

The remedy in this case and others is ruqyah as prescribed in
sharee’ah, which may be done by the sick person himself or by one who is
treating him, and it will be beneficial by Allaah’s leave. But it may need
to be repeated and you may need to do other things to help it. We will
mention the most important of these things here: 

1 – Reminding the sick person to always recite the adhkaar
for morning and evening, when going to sleep, eating, drinking, entering and
leaving the house, and to say a lot of dhikr in general. The best of dhikr
is reciting Qur’aan and the most important passages to recite are the
Mu’awwidhaat (soorahs seeking refuge with Allaah), al-Faatihah, Soorat
al-Baqarah and Aayat al-Kursiy. The more the sick person perseveres in
dhikr, the more the shaytaan’s influence on him will weaken, and he may be
expelled by means of ruqyah. 

2 – The ruqyah should be done by a righteous person who
adheres to the Sunnah and who shuns bid’ah, humbug and witchcraft. 

3 – The sick person should turn to Allaah a great deal and
ask Him for help, for Allaah answers the prayer of the one who is in
difficulty and relieves his distress, as He says (interpretation of the
meaning): “Is not He (better than your gods) Who responds to the
distressed one, when he calls on Him, and Who removes the evil, and makes
you inheritors of the earth, generations after generations? Is there any
ilaah (god) with Allaah? Little is that you remember!” [al-Naml 27:62].
Especially if the du’aa’ is offered at times when a response is more likely,
such as between the adhaan and iqaamah, just before dawn, in the last hour
after ‘Asr on Friday, when breaking the fast, and when travelling. 

4 – Always offering the five daily prayers on time. 

5 – Repenting to Allaah from sins that may be the cause of
the shaytaan gaining control of a person. 

6 – Purifying the house of things that the shaytaan loves,
such as images, dogs, music and singing. Imagine this devil being cornered and
having no food or drink or pleasure. He may be deprived of that by saying
the name of Allaah over food and drink and by getting rid of things that he
loves. Would he want to stay? 

For information on ruqyah as prescribed in sharee’ah, please
see the answers to questions no. 12918,
11290,
3476,
11026 and
21581. 

And Allaah knows best.