What are the legal rights of real daughter on father's property and assets after the death of father? In this case the father had second marriage with a lady who didn't had divorce with her first husband. What the law says?

 This case is a bit complicated. However, you have not mentioned whether the family is Hindu or Muslim, as the decision would be based on a different set of rules. If it's a Muslim family, the inheritance is governed by Muslim personal law. And if it's a Hindu family the inheritance will be governed by Hindu Succession Act.

However, in this case, the father’s second marriage is legally null & void since the lady didn’t have a divorce from her first husband. So her first marriage is still valid. As such her legal status actually is that of a mistress, not that of a wife. And mistress doesn’t have any legal right under any law in India.

Second marriage, during the subsistence of the first marriage, is illegal in India and the relationship arising from the same does not have any validity. Second wives in India have little protection under the law. With the commencement of the Hindu Marriage Act, 1955 (HMA), One of the conditions provided for a valid marriage was that neither party should have a spouse living at the time of the second marriage. Further, the lady has to prove her second marriage (socially or legally), but in doing so she will have trouble if her first marriage is brought to the notice and proved in the court of law. The lady would lose her case and could be charged with bigamy. However, the section will not apply if the husband or wife of the first marriage is dead. In case the second marriage is not legal, neither the second wife nor her children enjoy the privilege of being legal heirs to the ancestral property of the husband.

However, if the second marriage is proved legal then she will have equal rights as that of the daughter. In case the husband has left a will and the property is his self-earned, not inherited then his will has higher weightage even if he has willed the property to his wife (in this case mistress). But if the property is inherited, the daughter can challenge his will.

Now, married and unmarried daughters have the same rights on their father’s property as their brothers. They are also entitled to equal duties and liabilities as their brothers. In 2005, it was also ruled that a daughter has the same rights provided that both father and daughter were alive on September 9, 2005. In 2018, the SC stated that a daughter can inherit her deceased father’s property no matter whether the father was alive on this date or not. Hereon, women were also accepted as coparceners. They can demand a share in the father’s property.

As per the Hindu Succession Act – the heirs are classified into different categories. The following are classified as Class-I heirs, whose rights will have priority over other categories of heirs

i. Son ii. Daughter iii. Widow iv. Mother v. Son of a predeceased son vi. Daughter of predeceased son vii. Widow of predeceased son viii. Son of a predeceased daughter ix. Daughter of predeceased daughter x. Son of predeceased son of predeceased son xi. Daughter of predeceased son of a predeceased son xii. Widow of predeceased son of a predeceased son.

The Muslim laws in India are not codified laws and thus are governed by the 2 schools of Muslim Personal laws:-

Hanafi: Under Hanafi School, daughters do not have any right to their father's property. It recognizes only those heirs whose relation to the deceased is through a male child.

Shia: Under the Shia school, the daughters are given rights in the share of the property; they are given ½ of the share of the son in the property.

So basically, the daughter’s right to property under Muslim Law is given only under the Shia law.

Property rights of a daughter in Islam

Under the Muslim law, the rules of inheritance are rather strict. A son takes double the share of a daughter, on the other hand, the daughter is the absolute owner of whatever property she inherits. If there is no brother, she gets half a share. It is legally hers to manage, control, and dispose of it as and when she wants. She is also eligible to receive gifts from those she would inherit from. This is contradictory because she can inherit only one-third of the man's share but can get gifts without any hassle.

Widow’s right to succession:

Under Muslim law, no widow is excluded from the succession. A childless Muslim widow is entitled to one-fourth of the property of the deceased husband, after meeting his funeral and legal expenses and debts. However, a widow who has children or grandchildren is entitled to one-eighth of the deceased husband's property. If a Muslim man marries during an illness and subsequently dies of that medical condition without brief recovery or consummating the marriage, his widow has no right of inheritance.