Caution: Translations of Quran and Ḥadīth may lead to possible misapplications and misinterpretations. This site is intended for students of sacred knowledge that are proficient in comprehending classical Arabic and have a strong foundation in Islamic sciences. Also note that religious injunctions rely on several aspects beyond what one may glean through reading individual aḥādīth.
Qurʾān Bukhārī Muslim Nasāʾī Abū Dāwūd Tirmidhī Ibn Mājah Mālik Aḥmad Dārimī Ḥākim Ibn Ḥibbān Ṭabarānī Nasāʾī's Kubrá Bayhaqī al-Luʾluʾ wa-al-Marjān Ibn Rajab's Fifty Riyāḍ al-Ṣāliḥīn Aḥmad's Zuhd Suyūṭī

The child belongs to the husband

ahmad:10386 – Muḥammad b. Jaʿfar > ʿAwf > al-Ḥasan

it has reached me that the Messenger of Allah ﷺ decreed that the child belongs to the owner of the bed (husband) and the adulterer be stoned.   

أحمد:١٠٣٨٦ – حَدَّثَنَا مُحَمَّدُ بْنُ جَعْفَرٍ حَدَّثَنَا عَوْفٌ عَنِ الْحَسَنِ قَالَ

بَلَغَنِي أَنَّ رَسُولَ اللهِ ﷺ قَضَى أَنَّ الْوَلَدَ لِصَاحِبِ الْفِرَاشِ وَبِفِي الْعَاهِرِ الْحَجَرَ