A Muslim man married a non-Muslim woman, who at the time of their marriage reverted to Islam but continued going to Church etc. They later had a daughter but the father died while she is still young. She is grown up now but followed the religion of her mother. Does she any claim to her father’s estate being that he died while she was still a child?
بسم الله الرحمن الرحيم
If any of the spouses commit apostasy the Nikah will be terminated. The couple must separate, as all relations thereafter become prohibited (i.e., it will be considered adultery and fornication). However, if a child is produced from such a union, paternity will only be established if the child is born two years or less from the time of apostasy. But if a child comes after two years, paternity will not be established. Thus, the child will have no real father, rather he will be attributed only to his mother and her relations.
A Muslim who leaves the fold of Islam will not be attributed to the religion in which he or she entered into, rather he or she will be regarded as an apostate and the laws of apostasy will apply to him.
In principle a man is allowed to marry a Christian woman. If, however, she accepts Islam thereafter reverts to Christianity the laws relating to the People of the Book would not apply to her, rather she is considered an apostate [and not a Christian/Kitaabiyah].
In a marriage, if one of the parents is a Muslim and the other isn’t,  the non-baligh children will be considered Muslims and the laws of Islam in every aspect will apply to them.
With regards to your specific query, there are two possibilities;
- The wife accepted Islam sincerely with the intent of being a Muslim. Thereafter, she denounced Islam and reverted to Christianity. That being the case, the aforementioned rules would apply i.e. the paternity of the daughter will only be established if the daughter was born two years or less from the time of apostasy. Furthermore, upon death of her father, she will inherit from his estate. If, however, the couple lived together after the apostasy of the wife and the daughter came after two years [from the time of apostasy], her paternity will not be established and hence she will not be entitled to inheritance from the estate of her biological Muslim father.
- The wife did not accept Islam rather she uttered the Shahadah for merely for ceremonial reasons (i.e. for the marriage proceedings), then she will not be regarded a Muslim. Rather she will still be considered a Christian (Kitaabiya). As stated above, it is allowed for a Muslim man to marry a Christian woman (though strongly discouraged). Nevertheless, the relations will be Halal, the paternity of the children will be established and the non-baligh children will be Muslims. This being the case, the daughter will inherit from the estate of her
The Prophet ﷺ said that a Kafir does not inherit from a Muslim. In the above scenario, the daughter will still be entitled to inheritance as she was a Muslim at the time of the demise of her father. It is worth noting that according to the Shariah, the daughter is also considered an apostate as she was Muslim who thereafter changed her religion.
Nb: In none of the two above scenarios will the wife inherit from the estate of her deceased husband.
And Allah Ta’ala Knows Best
Mufti Kaleem Muhammad
Darul Iftaa, Jaamia Madinatul Uloom
 المبسوط للسرخسي (17/ 132)
قال: وإذا ارتد أحد الزوجين والعياذ بالله فإن الولد يلزم الزوج إلى سنتين؛ لأن الفرقة وقعت بردة أحدهما بعد الدخول وهو موجب للعدة عليها فإذا جاءت بولد في مدة يتوهم أن العلوق حصل في حال النكاح يثبت النسب منه كما لو وقعت الفرقة بالطلاق، وكذلك لو لحق بدار الحرب مرتدا؛ لأن المرأة لما بقيت في دارنا فهي مؤاخذة بأحكام الإسلام فعليها العدة إلا أن نسب ولدها لا يثبت من الزوج عند أبي حنيفة – رحمه الله – بشهادة القابلة ما لم يشهد به رجلان أو رجل، وامرأتان؛ لأن المقصود هو الميراث، ولا يثبت الميراث بشهادة المرأة الواحدة وعندهما شهادة القابلة كافية، وأصله في مسألة كتاب الطلاق إذا لم يكن هناك حبل ظاهر، ولا فراش قائم، ولا إقرار من الزوج بالحبل لا يثبت النسب عند أبي حنيفة – رحمه الله – إلا بشهادة شاهدين وعندهما يثبت بشهادة امرأة واحدة
 E.g. Muslim husband and Kitababiya wife or one spouse from a non- Muslim couple accepts Islam.
 Many Muslims conducting marriages wrongfully assume the legitimacy of a Muslim man marrying a non-Muslim woman provided that she utters the Shahadah at the time of marriage. The woman has no intention of accepting Islam, rather her utterance of the Shahadah is merely for ceremonial purposes.
 الدر المختار وحاشية ابن عابدين (رد المحتار) (6/ 767)
(قوله فأسلمت) أي بعد موته، فلو قبله فالظاهر أن الحمل لا يرث قولا واحدا لأنه جزء منها فهو مسلم عند موت المورث وعند الولادة تبعا لها: وهي واقعة الفتوى
 The wife will only inherit in the first scenario if she was still a Muslim when her husband died i.e. her apostasy came after the demise of her husband. However, from the query, this possibility seems highly unlikely.