Will the child of fornication intercede for his mother on the Day of Resurrection if he dies before birth, and will he be counted among the righteous?

There is no text regarding the intercession of a stillborn child born of adultery. However, there is the general hadith about the miscarriage (al-siqt), which indicates that the miscarriage will draw its mother into Paradise if she seeks recompense from Allah for it.

As for whether it is among the righteous, it is indeed so because it died before reaching the age of accountability (takleef), committed no sin, and does not bear the burden of its parents, as Allah the Almighty says: "And no bearer of burdens will bear the burden of another," and as the Prophet, peace and blessings be upon him, said: "The child of adultery does not bear any of the burden of its parents."