You are asking for the Lateral Entry Entrance Test B.Tech colleges and entrance exams in India. Here I am provide you information about this. This is as follows:

List of Engineering Lateral Entry Entrance Exams:

AIEEE All India Engineering Entrance Exams
Calicut University Lateral Entry Entrance Exams
Delhi technical University Lateral Entry Entrance Examination
Kerala University Lateral Entry Exam
KIIT University Lateral Entry Entrance Examination
Lateral Entry Entrance Test LEET
LPU NEAT (National Engineering Aptitude Test)
MITManipal BE Lateral Entry Entrance Exam
Mumbai University Lateral Entry Entrance Examination
Punjab Technical University Lateral Entry Entrance Test (PTU LEET)
UKSEE B.Tech (Lateral Entry) Entrance Exam
Uttarakhand Technical University Lateral Entry Entrance Test
West Bengal University Joint Entrance Exam for Lateral Entry (JELET)

List of major institutions/Universities that take part in these Entrance Exams:

Amity School of Engineering
Amrita Institute of Technology & Science
Cochin University, Cochin
CUSAT Kochi
Dharmsinh Desai Institute of Technology
Dhirubhai Ambani IICT Gandhinagar
Faculty of Engineering and Technology, Jadavpur University, Kolkata
G.H. Patel College of Engg & Technology
Guru Nanak Dev Engg College Ludhiana
Harcourt Butler Technological Institute Kanpur
Hindustan Institute of Technology, Chennai
IIIT Allahabad
Indraprastha University, New Delhi
Institute of Technology, Nirma Univ, Ahmedabad
International Institute of Information Technology, Hyderabad
Jabalpur Engineering College
Jamia Millia Islamia, New Delhi New Delhi
JNTI Hyderabad
Kalinga Institute of Industrial Technology Bhubaneshwar
KIITS Orissa
M.S. Ramaiah Institute of Technology
M.S. Ramaiah Institute of Technology Bangalore
Maharashtra Institute of Technology (MIT)
MNIT Jaipur
St. Longowal Institute of engineering and tech., Punjab
VIT Vellore