respected querist,
first method, submit a application alongwith an affadavit and supporting documents regarding the correct name of your father to the issuing authority or education board regarding the request of correction of your fathers name .but sometimes authorities shows their unablity to do so then you have to file a declaration suit in the civil court regarding the accurate name of your father making the issuing authority and board a defendents ,after obtaining the favourable order the borad and issuing authority of your certificate will become bound to make the requisite changes.feel free to call if yo had left any doubt.
respected querist ,you dnt have to make publication yourself ,i told you already it is the process of civil litigation and court will order you during th eprocess to deposite the charges for it and publication will get intructed on the instructions from the court and by the court,you dnt have to do it at your own wish,this is no where relating to the passport,to know the passport process better kindly read the passport authority act 1976.