1. As per your narration it is understood that your father being the absolute owner of the property died intestate.
2. Assuming that you two brothers are the only children to your parents, the property would devolve equally to your mother, you and your brother, i.e., 1/3rd share each.
3. After your father's death the flat was registered in your mother's name after you and your brother provided NOC to TNHB.
4. Even though your mother's name is there in the official records, she only has 1/3rd share in the property as also her children. Your giving NOC along with your brother to TNHB does not release you and your brother's rights in your mother's favour.
5. To resolve this issue, you brothers can sign the sale deed as Vendors, along with your mother or you brothers can execute a 'Release Deed' in favour of your mother so that she can sell the property on her own without your giving NOC to the buyer.