I was Additional Director of Ex-Servicemen's Welare, Tamil Nadu Govt. Mr.Kalaselvan's comments are correct. However, if your father died while in service of the Bank, dependent on that Bank's policy, you may be able to get compassionate appointment with them. Kindly approach the District Solder's, Sailors' & Airmen's Board of your District for further clarifications.
There are some reservations in Educational Institutions for Children. Your Mother will be entitled to Canteen Facility.