I am a married lady with three children (all boys). Is it permitted in Islam to use scientific methods to select the gender of my future children? I would like to have a girl and fear that if I don't do this I may end up with no daughters at all. Would you please provide the evidence for your answer in case it is not permitted?

Praise be to Allah, the Lord of the World; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Selecting the gender of a fetus is possible only through the procedure of isolation and separation of one's semen. The woman who can not give birth normally undergoes the procedure of artificial fertilization.
The artificial fertilization procedure has many dangers and prohibitions, such as uncovering the body, even the private parts of the woman, and the probability of mixing the spermatozoid of her husband with someone else's spermatozoid, etc.
Therefore, we had the opinion that the separation of semen to select the sex of a future baby or artificial fertilization is not permissible as long as the person is capable to give birth normally. In fact, artificial fertilization is permitted only to the woman who can not give birth normally and provided she takes into consideration the conditions and precautions mentioned in the Fatwa: 81889, 82551 and 82554.
It is proved through research that eating certain foods helps in selecting the gender of the baby.
Finally, we advise you to accept happily what Allah grants you and seek only good pious children. It is very possible that a male child can be a greater source of happiness than a female child, or vice versa. Not every man is good nor is every woman bad.
Allah knows best.