The current imam of the time is Imam Al-Mahdi who is the 12th imam and the son of the 11th imam, Imam Hassan Al-Askari.
We have many authentic and reliable ahadith relating to the matter of the 12th imam. Allah swt also prolonged his age just like He did with previous prophets.
Inshallah soon I will release a translation of a book being worked on relating to authentic ahadith on this matter.
About some Ismailis, although their imam of the time would be the current Agha Khan, for the 12er Shias, he is a false imam who shouldn’t be followed. The Bohra Ismailis also follow a different imam and have their daei’ mutlaq.
One may also notice that the Ismaili Agha Khanis have abandoned all shariah practices because of their current imam. For example many Ismailis do not fast, pray like Muslims do, perform hajj, wear hijab, focus on tahara or many other important jurisprudential issues.
We ask Allah to guide them and us all