Short answer
Yes, as a word of affection, when everyone knows who the real father is. The Prophet ﷺ called young Anas "my son". What is forbidden is giving the child the stepfather's lineage, for example as "son of" him in their legal or religious name. The four schools agree.
Calling an older man "father", or a child "my son" or "my daughter", out of love or respect is permissible. Ascribing lineage to him, so that the child is named or registered as his child, is haram.
The four schools agree on this.
Explanation
The Quran ended adoption as a change of lineage, and the Prophet ﷺ warned against claiming a father who is not your own. But the same Prophet called Anas ibn Malik "ya bunayya", my little son, though Anas was not his son. Arabic, like English, uses family words for love and respect: "uncle" for an elder, "sister" for a friend. The scholars of the four schools distinguish this from lineage.
Allowed:
- A child calling a stepfather, foster father or adoptive father "Dad", "Baba" or "Abbu" at home.
- A stepfather calling his stepson "son".
- Introducing them in everyday speech as "my son" when the real lineage is known and recorded.
Not allowed:
- Changing the child's name to "bin" or "bint" the stepfather, or giving the child his surname so that it reads as lineage. See the adopted child's surname.
- Hiding the birth father so the child grows up believing the stepfather is the father. See telling a child they are adopted.
- Naming the stepfather as father in a nikah or other place where lineage decides the ruling.
Mahram: a stepfather is a permanent mahram to his stepdaughter once he has consummated the marriage with her mother, so hijab rules do not apply between them. An adoptive father is not a mahram by adoption alone; see is an adopted child mahram.
The evidence
Quran, Surah Al-Ahzaab 33:5
ٱدْعُوهُمْ لِءَابَآئِهِمْ هُوَ أَقْسَطُ عِندَ ٱللَّهِ ۚ فَإِن لَّمْ تَعْلَمُوٓا۟ ءَابَآءَهُمْ فَإِخْوَٰنُكُمْ فِى ٱلدِّينِ وَمَوَٰلِيكُمْ ۚ وَلَيْسَ عَلَيْكُمْ جُنَاحٌۭ فِيمَآ أَخْطَأْتُم بِهِۦ وَلَٰكِن مَّا تَعَمَّدَتْ قُلُوبُكُمْ ۚ وَكَانَ ٱللَّهُ غَفُورًۭا رَّحِيمًا ﴿٥﴾
Call them by [the names of] their fathers; it is more just in the sight of Allah. But if you do not know their fathers - then they are [still] your brothers in religion and those entrusted to you. And there is no blame upon you for that in which you have erred but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful.
Lineage belongs to the real father.
Quran, Surah An-Nisaa 4:23
حُرِّمَتْ عَلَيْكُمْ أُمَّهَٰتُكُمْ وَبَنَاتُكُمْ وَأَخَوَٰتُكُمْ وَعَمَّٰتُكُمْ وَخَٰلَٰتُكُمْ وَبَنَاتُ ٱلْأَخِ وَبَنَاتُ ٱلْأُخْتِ وَأُمَّهَٰتُكُمُ ٱلَّٰتِىٓ أَرْضَعْنَكُمْ وَأَخَوَٰتُكُم مِّنَ ٱلرَّضَٰعَةِ وَأُمَّهَٰتُ نِسَآئِكُمْ وَرَبَٰٓئِبُكُمُ ٱلَّٰتِى فِى حُجُورِكُم مِّن نِّسَآئِكُمُ ٱلَّٰتِى دَخَلْتُم بِهِنَّ فَإِن لَّمْ تَكُونُوا۟ دَخَلْتُم بِهِنَّ فَلَا جُنَاحَ عَلَيْكُمْ وَحَلَٰٓئِلُ أَبْنَآئِكُمُ ٱلَّذِينَ مِنْ أَصْلَٰبِكُمْ وَأَن تَجْمَعُوا۟ بَيْنَ ٱلْأُخْتَيْنِ إِلَّا مَا قَدْ سَلَفَ ۗ إِنَّ ٱللَّهَ كَانَ غَفُورًۭا رَّحِيمًۭا ﴿٢٣﴾
Prohibited to you [for marriage] are your mothers, your daughters, your sisters, your father's sisters, your mother's sisters, your brother's daughters, your sister's daughters, your [milk] mothers who nursed you, your sisters through nursing, your wives' mothers, and your step-daughters under your guardianship [born] of your wives unto whom you have gone in. But if you have not gone in unto them, there is no sin upon you. And [also prohibited are] the wives of your sons who are from your [own] loins, and that you take [in marriage] two sisters simultaneously, except for what has already occurred. Indeed, Allah is ever Forgiving and Merciful.
A stepdaughter becomes forbidden in marriage, so the stepfather is her mahram.
Sahih Muslim 2151
Sahih... قال لي رسول الله صلى الله عليه وسلم يا بني ...
"The Messenger of Allah said to me: O my son."
Calling a child "my son" out of affection is not claiming lineage.
Where the ruling is recorded
- al-Minhaj Sharh Sahih Muslim (al-Nawawi), Kitab al-Adab, chapter on calling someone else's child "my son". It is permitted as kindness.
- al-Hidaya, Kitab al-Nikah, chapter on women one may not marry. A stepdaughter is forbidden once the marriage with her mother is consummated.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.