You are entitled to get a compassionate appointment under the Uttar Pradesh Recruitment of Dependents of Government Servants Dying-in-Harness Rules, 1974. Article 16 of the constitution of India provides equality of opportunity in respect of government service. But the compassionate appointment does not come under the purview of public appointment.
Compassionate appointment serves a social purpose i.e. to provide ameliorative relief to the family of a government servant who has died in harness.
In Union of India v. Shashank Goswami and another, AIR 2012 SC 2294 the Hon’ble Supreme Court has observed that the compassionate appointment cannot be claimed as a matter of right.
Your mother is dependent upon you because her financial condition became weak after the death of her husband. In this condition you, as a child, can extend the financial support to your mother. You are also facing financial hardship. In this circumstance you are entitled to get a compassionate appointment.
There is no difference between a son and married daughter in respect of granting compassionate appointments. In Isha Tyagi vs. State of U.P  the Allahabad High Court has held that
If the marital status of a son does not make any difference in law to his entitlement or to his eligibility as a descendant, equally in our view, the marital status of a daughter should in terms of constitutional values make no difference.
In Smt. Vimla Srivastava vs State Of U.P. And Another  the Allahabad High Court has held that a married daughter is also entitled to get compassionate appointment because she comes under the meaning of “family” under n Rule 2 (c) of the Dying-in-Harness Rules 1974.
You should file a writ petition before the High Court under article 226 of the constitution of India. In that writ petition you should seek a direction from the High Court for providing you the benefit of compassionate appointment.