Praise be to Allah.
Saying Bismillaah at the time of intercourse is mentioned in the hadeeth of the Prophet (peace and blessings of Allaah be upon him): “If one of you says, when he has intercourse with his wife: ‘Bismillaah, Allaahumma jannibni al-Shaytaana wa jannib al-Shaytaana ma razaqtana (In the name of Allaah, O Allaah, keep the Shaytaan away from me and keep the Shaytaan away from that which You bestow upon us),’ if it is decreed that they should have a child, the Shaytaan will never harm him.”
Narrated by al-Bukhaari, 5165; Muslim, 1434.
With regard to how this benefits the child, the scholars differed as to what is meant by the words of the Prophet (peace and blessings of Allaah be upon him), “the Shaytaan will never harm him.” There are many opinions:
1- That what it means is that the Shaytaan will not control him because of the blessing of saying Bismillaah, rather he will be one of the people of whom it was said: “Certainly, you shall have no authority over My slaves” [al-Hijr 15:42].
2- It means that he will never harm him physically.
3- It means that this is a means of his being protected from shirk and kufr.
4- It means that he will keep away from major sins.
5- And it was said that he will not be harmed by the Shaytaan’s participation in his father’s having intercourse with his mother, as it was narrated that Mujaahid said: The one who has intercourse and does not say Bismillaah, the Shaytaan wraps himself around his penis and has intercourse along with him.
Ibn Hajar said: Perhaps this is the most correct answer. But the first answer may also be correct, especially since we know that many people who know about the great blessing of saying Bismillaah may forget all about it at the time of intercourse, and for the few who may remember it and say it, pregnancy may not occur. If this is very rare, then it is possible that the first answer may be correct.