Can a bastard child inherit from his father? If no why? Please give me authorities from Qur'an, Sunnah and other relevant Islamic sources.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

The child of Zina (who was born outside wedlock) is traced back to his mother's lineage and to her family. The rulings of Mahram apply to him in relation to his relatives from the mother's side only. His/her legal Wali is from the mother's side and he inherits from that side which is the only one that inherits from him and to which he is legally linked. So, all other rulings concerning fatherhood stem directly from the mother's side. Therefore, the child born outside legal wedlock is not traced back to his father, nor does any of them inherit from the other. This is the most preponderant opinion and it is the opinion of the majority of the scholars.

Some scholars, however, believe that he can be traced to his father if the latter accepts him as his son. This is the opinion of Is-Haaq Ibn Rahawayh, ‘Urwah, Sulaymaan Ibn Yasaar and Abu Haneefah. Imam Abu Haneefah says: “I do not find any harm that a man who commits Zina (adultery or fornication) with a woman and she gets pregnant as a result, that he protects the honor of this woman by marrying her and the child is his.”

But there is sound evidence backing the opinion of the majority of the scholars which is the judgment reported from the Prophet about the child of Zina: “The Prophet decided regarding one who was treated as a member of a family after the death of his father, to whom he was attributed when the heirs said he was one of them, that if he was the child of a slave-woman whom the father owned when he had intercourse with her, he was included among those who sought his inclusion, but received none of the inheritance which was previously divided; he, however, received his portion of the inheritance which had not already been divided; but if the father to whom he was attributed had disowned him, he was not joined to the heirs. If he was a child of a slave-woman whom the father did not possess or of a free woman with whom he had illicit intercourse, he was not joined to the heirs and did not inherit even if the one to whom he was attributed is the one who claimed paternity, since he was a child of fornication whether his mother was free or a slave.” [Ahmad, Abu Daawood, Ibn Maajah and Ad-Daarimi]

Allah knows best.