Hello Abhishek; 
Government Engineering colleges in Andhra Pradesh are as; 
1. Andhra University College of Engineering, Visakhapatnam 
2. Jawaharlal Nehru Technological University
3. National Institute of Technology,  Andhra Pradesh 
4. Indian Institute of Technology, Tirupati 
5. Acharya Nagarjuna University , Guntur

Just click on the below link for more information
Link here; the government engineering college in Andhra Pradesh :  https://engineering.careers360.com/colleges/list-of-government-engineering-colleges-in-andhra-prades
Hope it helps. 
Thank you 

Hello Abhishek

In Andhra Pradesh most of the engineering colleges gives admission on the basis of AP EAMCET , there are very few colleges consideing JEE mains.

Top Government Engineering Colleges in Andhra Pradesh are:

• Andhra University College of Engineering, Visakhapatnam
• JNTUA College of Engineering, Anantapur
• Jawaharlal Nehru Technological University College of Engineering, Kakinada
• Indian Institute of Petroleum and Energy Visakhapatnam
• Indian Institute of Technology Tirupati
• JNTUA College of Engineering, Pulivendula
• JNTUK University College of Engineering, Vizianagaram
• National Institute of Technology Andhra Pradesh
• Sri Venkateswara University, Tirupati

However for detail knowledge of government engineering colleges, you can copy -paste below link:

https://engineering.careers360.com/colleges/list-of-government-engineering-colleges-in-andhra-pradesh

THANKYOU 

please upvote

Top Government Engineering Colleges in Andhra Pradesh are:

• Andhra University College of Engineering, Visakhapatnam
• JNTUA College of Engineering, Anantapur
• Jawaharlal Nehru Technological University College of Engineering, Kakinada
• Indian Institute of Petroleum and Energy Visakhapatnam
• Indian Institute of Technology Tirupati
• JNTUA College of Engineering, Pulivendula
• JNTUK University College of Engineering, Vizianagaram
• National Institute of Technology Andhra Pradesh
• Sri Venkateswara University, Tirupati
• You can open this link to find  more about them https://engineering.careers360.com/colleges/ranking/top-government-engineering-colleges-in-andhra-pradesh