These students, hailing from Andhra Pradesh or Telangana, had left for the US on December 29 to pursue higher education at Silicon Valley University and Northwestern Polytechnic University there.
National carrier Air India had earlier said it had received a communication from the US Customs and Border Protection Agency that these two universities were "under scrutiny" by authorities in that country.
"US officials (at New York Airport) asked us to get admission to some other university and apply for visa (afresh). They say these (two) universities are not good," said a student, who had enrolled in Northwestern Polytechnic University, on the condition of anonymity.
"They (US authorities) said we should voluntarily cancel the admissions or they will deport us back. We have valid visas...When we sought to know the reasons for not allowing us in the country, they threatened they would revoke our visas," another student, a B-Tech degree-holder from Guntur district of AP, told reporters.
"Some of the male students were handcuffed while being taken from one terminal to another. Our documents are original and in order. There is no fault from our side," said another student.