As-Salam aleikum wa rahmatullahi wa baraketuh,
In regards to the claim that Jesus (pbuh) visited India, it is possible, but to say that he studied there Buddhism and preached it in Israel is an absurd and against the monotheistic prophethood as well as the teachings of Allah SWT.
There are few internal and external evidences which may indicates in some points that Jesus (pbuh) travelled to India, probably looking for the lost sheeps of Israel.
Firstly, it can be noticed that the New Testament tells nothing about the life and ministry of Jesus (pbuh) between the ages of 14 and 29. Thus, many scholars and historians asked where he have been and what he was doing in this period ?
There is a book written by Nicolas Notovitch, a Russian-Jewish journalist and adventure who claimed that during his trip in India, he have found an ancient document that reportedly contains a conversation between a Buddist King and an Israeli prophet named Isa and that the Church - specifically the Vatican - deliberately hiding this truth because it reveals inconvenient information. This could be true since the Church never refers to Jesus (pbuh) as Isa, only the Quran!
Here is the book of Nicolas Notovitch:
https://archive.org/details/unknownlifeofjes00notorichHowever, some modern scholars like Wilhelm Schneemelcher, Bart D. Ehrman, Gordon Stein, Robert M. Price called it a hoax and that his story is not based on facts.
Secondly, Eusebius (ca. 264-340 A.D.) writes that according to one of the traditions, the Apostle Bartholomew
left in India a Hebrew version of Matthew's Gospel. Eusebius writes further that around the year 200 A.D. Pantaenus the Philosopher, on his mission to India, indeed have found there
the Gospel of Matthew in Hebrew letters. Eusebius is convinced that it was Bartholomew the Apostle, who took it there. A similar story gives Jerome (d. 420 A.D.), another early church father.
Now, critically thinking, if the Notovitch whole story about his travel experiences in India is a lie and invention (as some scholars have said), we should ask why 2000 years ago, one of Jesus’s disciples went on a long journey to India (a place situated maybe over 2000 km from the borders of Palestine) just to bring there a Hebrew Gospel of Matthew ?? Certainly the Apostles have preached the Gospel in various countries, but
was there some Hebrew speakers in India ? It would make sense only if we assume that the lost tribes of Israel was found there, although it is difficult for me to say whether this info are correct.
By the way, it is curious that according to some hadith, Adam (pbuh), after committed a sin by eating from the forbidden tree, Allah SWT send him into India. Now, the Quran says that Jesus (pbuh) is like Adam (pbuh), of course in the way of creating these two, but the fact itself that Adam (pbuh) was brought to India is interesting if we accept the view the Jesus (pbuh) too went there in his lifetime.
Allah knows best!
Take care, and salam
Ahmed (Poland, Warsaw)