Hisham narrates from his father that Sayyidah Aishah (may Allah be pleased with her) said concerning the child born of fornication: Nothing of his parents' burden is upon him: "No soul will bear the burden of another." [Surah Fatir: 18]
Some weak narrators attributed it to the Prophet (marfu'), but the correct view is that it is mawquf (her own saying).
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الأيمان / 19992