I am enlisting down some government college which will be good for B.Tech Lateral Entry :-

• Bundelkhand Institute of Engineering & Technology, Jhansi
• Indian Institute of Carpet Technology, Bhadohi
• Institute of Engineering and Technology, Lucknow
• Kamla Nehru Institute of Technology, Sultanpur
• Uttar Pradesh Textile Technology Institute, Kanpur
• Bipin Tripathi Kumaon Institute of Technology, Dwarahat
• College of Basic Sciences and Humanities, Pantnagar
• College of Technology, Pantnagar (Pant Nagar University)
• G.B. Pant Engineering College, Ghurdauri, Pauri Garhwal
• APJ Abdul Kalam Institute of Technology, Tanakpu
• Assam Engineering College, Guwahati
• Jorhat Engineering College, Jorhat
• Central Institute of Plastic Engineering and Technology, Patia, Bhubaneshwar
• College of Engineering and Technology, Ghatikia, Bhubaneshwar

There is no any national level exam for B.Tech Lateral Entry programme but yes there are some state level entrance exams which you have to clear to get admission to direct second year of B.Tech like AP ECET, TS ECET, JELET, OJEE Lateral entry and so on.

For more details refer to the link given below :-

https://engineering.careers360.com/articles/b-tech-lateral-entry-in-government-college

I hope this information helps you.

Good Luck!!