I'm learning Democratic Politics in 9th Grade. I had this doubt for a long time.
Can an Indian President/Prime Minister send someone to jail without filing a case?
No. Neither the President nor the Prime Minister can arbitrarily detain someone without cause.
Article 21 of the Constitution of India prohibits arbitrary detention:
No person shall be deprived of his life or personal liberty except according to procedure established by law
Article 20(1) prevents punishment for something that only becomes a crime later:
No person shall be convicted of any offence except for violation of a law in force at the time of the commission of the Act charged as an offence, nor be subjected to a penalty greater than that which might have been inflicted under the law in force at the time of the commission of the offence.
And Article 22(2) requires detainees to be put in front of a magistrate shortly after their arrest, except in certain circumstances:
Every person who is arrested and detained in custody shall be produced before the nearest magistrate within a period of twenty-four hours of such arrest excluding the time necessary for the journey from the place of arrest to the court of the magistrate and no such person shall be detained in custody beyond the said period without the authority of a magistrate.
It is worth noting that Article 359 allows for the President can suspend enforcement many rights in a State of Emergency, but these rights are not among those than can be suspended.
Jail is a vague term.
There is preventive detention, where the police can detain you to prevent you from doing some harm. Special cases.
There is remand and custody when the police is investigating a case and someone is a prime suspect.
A political leader may hypothetically exert influence over government servants under him to take a person in preventive detention or to take a person under custody for some criminal charge(genuine or bogus). But a prison sentence can only be awarded by a court of law.
Habeus Corpus is a fundamental right, which stipulates that police has to give reasons for detaining someone. But in special circumstances like a National Emergency etc.(or Martial Law) police powers can see wide expansion and police can detain people for little reason.
Also, this question is more suited for Law Stack Exchange I feel.