The Deputies of Imam Mahdi (pbuh) were:
Ghaybate kubra started from the death of his 4th deputy till this day.
During Ghaybate sughra ( short occultation ) although the Muslims could not see Imam (A) they could communicate with him through his deputies:
Uthman bin Said
Muhammad bin Uthman
Husain bin Rauh
Ali bin Muhammad Samry.
During Ghaybate kubra ( long occultation ) although there are no special deputies. The Mujtahids are his representatives.
Useful information: The duties of each and every Muslim in the time of Ghatbate kubra is:
To be the caretakers of Islam.
To pray for the safety of Imam (A) and give sadaqa for his safety.
Ask Allah to make Imam (A) appearance soon, so that he may come and fill the world with truth and peace.
Whenever the name of the12th Imam is said, you should stand, placing your right hand on your head and bow your head. You should also recite Salawaat after his name.
Moral:
The Holy Prophet (S) has said that if someone dies without knowing the Imam (A) of his time, his death is that of an unbeliever. We must therefore carry out our duties to our 12th Imam who is still alive and in Ghaybate(concealment).