Sayyidah Aishah Siddiqah (may Allah be pleased with her) reports this saying of the Prophet (peace and blessings be upon him): "Nothing of the sins of his parents applies to a child born of fornication." Then he recited this verse: "No bearer of burdens will bear the burden of another."
Al-Tabarani recorded it in al-Mu'jam al-Awsat. Its chain contains Ja'far bin Muhammad bin Ja'far al-Mada'ini, and I do not know him.
Hadith Referenceمجمع الزوائد ومنبع الفوائد / كتاب الحدود والديات / 10554