All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
May Allaah reward you best and bless you for consulting the scholars regarding this serious matter as well as for your keenness to clear yourself of liability of anything that may expose you to punishment in the Hereafter. As for the answer to your question, the scholars unanimously agree that it is prohibited to fulfill a vow of slaughtering one's son. Even more, fulfilling this vow is one of the gravest major sins, as it implies killing a person without a Sharee'ah-approved reason. Allaah Almighty says (what means): {But whoever kills a believer intentionally—his recompense is Hell, wherein he will abide eternally, and Allaah has become angry with him and has cursed him and has prepared for him a great punishment.} [Quran 4: 93]
No fulfillment is due for this vow because it is prohibited. It was narrated on the authority of ‘Aa’ishah that the Prophet, sallallaahu ‘alayhi wa sallam, said: "Whoever vowed to obey Allaah, let him do so; and whoever vowed to disobey Him should not do it." [Al-Bukhari]
As for the command of Allaah, the Exalted, to Prophet Ibraaheem (Abraham) to slaughter his son, it was specific to him as a trial and test. Allaah says (what means): {Indeed, this was the clear trial. And We ransomed him with a great sacrifice.} [Quran 37: 106-107] This is something exclusive to Ibraaheem and it is not applicable to others. So we seriously warn you not to fulfill this vow. It is a void vow, which entails nothing to be done on your part. Some scholars, however, hold the opinion that you are required to slaughter a sheep, as Prophet Ibraaheem did. This is also the opinion of Ibn ‘Abbaas .
Allaah Knows best.