Sayyiduna Ali and Sayyiduna Abdullah (may Allah be pleased with them both) said: The 'asabah (residuary heir) of the son of a couple who performed li'an is his mother; she inherits all of his wealth. If he has no mother, then her 'asabah are his 'asabah, and the child of fornication is in the same position. Sayyiduna Zayd bin Thabit (may Allah be pleased with him) said: For the mother is a third, and the rest goes to the public treasury (bayt al-mal).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12492