compassionate Appointment

Yes, you are entitiled for appointment on compassionate ground. You should apply as soon as possible. Actually Mr. Raja, appointment rules changes from State to State and Company to Company. Usually, in such matters elder child is entitled like in your case you. However, you should not be engaged in any type of business or job to claim appointment on compassionate ground. You give request to the Company let them reply. Then, you may require legal help. I think, Right now, you didn't applied for it. So, this is premature stage.  

1st thing 1st.

Download 'Compassionate Employment ' rules and policy of the establishment and go thru it carefully.

Apply as per policy and rules under proper acknowledgment, in time and without delay.

Post facts only in the application.

If you find any difficulty in understanding show the rules and policy to senior colleagues of your father, seasoned employees/trade union leaders, local counsels .................. 

If you wish you may atatch the rules and policy in the thread or post the weblink, to get response.

These may be available on website of establsihment or in office.

Collect the copy and required forms.

While posting queries don't post short forms,abbreviations, and post full forms.

If the establishment offeers 'Solatium'; one time compensation, then post back. 

No proper views can be formed.

You nowhere stated how old is the death and what are familyassetts and who are other claimnats for the job.