Who are the Legal heir of a spinster

In the case of a spinster, if no will is made by her, the Legal heir will be her parents.
In case if the parents are not alive, her siblings will be the legal heirs.
If she makes a will, the property will go to the person whom she mentioned in her will.
All the siblings will have equal rights. If any sibling is not alive his. that sibling's legal heirs will become the owners of her part. They can claim their share anytime. This is as per the Hindu Succession Act.
If there are no legal heirs the assets will go to the government.
In your case also any of the legal heirs of the siblings of your aunt can file a case against the share of them from her property.

According to the Hindu Succession Act (Amendment 2005) who is the legal heir:
Your aunt had died as intestate and unmarried, so her parents are the first legal heir for her property. If her parents have also died then her siblings are the legal heirs. Since your father and your elder aunt are the only alive siblings of your aunt then both of them are legal heirs of her property. Your father needs the succession certificate to prove that he is the legal heir of the deceased.
Her nephews and nieces are not legal heirs.

While considering the case of spinster, the property would go to the parents as they are the legal heirs. In case the parents are no more, her siblings would enjoy the property. In that situation, the property is to be divided among the number of siblings of the dead parents.
In case of availability of a will, the property would go in favour of the person/ persons recommended by her.
Here one point is to be noted, all the siblings are entitled to get equal shares of the existing property. It may so happen that some of the siblings are dead and in that circumstances, the legal heirs would be their children. This is within the compliance of Hindu Succession Act as amended in 2005.
As per your submission, your father and your aunt are the only survivors as the legal heirs, they can claim the property with the production of the succession certificate released by the court.

According to Hindu property law, when no person has been declared the heir to the property of any woman and if the woman dies, the following will be divided among the heirs and the order of preference will be the following:

1. First preference will be given to son and daughter - If the woman is married and has children, the first right over her property is with her son and daughter.
2. Other heirs of the husband - If this is the child, then the other heirs of the husband will be given that property.
3. Right to the right of father and mother - If the woman is not married at all, she has an adopted child, then in that case the right to the property of the woman will be that of her guardian.
4. Other heirs of the father - If both the mother and father of the woman are not alive then the property will be distributed among the heirs of the father of the woman. The same law will apply in your case. Since your sister used to live with you and they do not have any other family, then the right to property will be yours.
5. Heir to the mother - If there is no heir in favor of the woman's father, then in the end this property will be divided among the heirs of the mother of the woman.

For a person belonging to Hindu religion this would be dealt as per the Hindu Succession Act, 1956. You have mentioned that your aunt died as a spinster and she had not made any will for her property or other assets that she possessed.
As per the Hindu Succession Act, 1956 the legal heirs are categorised in two distinct classes known as Class I and Class II. Under class I, the parents of the spinster would come in case they are alive. If they are not alive then the legal heir right shifts to the other contenders falling under class II that is the siblings. If siblings are alive it will go to them as per the equitable distribution. If some siblings are alive and some are not alive then it will be passed on to the existing siblings and children of the deceased siblings like you. So you can draw the family tree and visually see the relationship of the existing people with the deceased aunt. It will help in understanding the legal heir rights more clearly.