Dear Karthik,
The best private universities in India which offers BSc Agriculture course are




1. DR.YSR HORTICULTURAL UNIVERSITY, TADEPALLIGUDEM
2.  S. V. AGRICULTURAL COLLEGE - [SVAC], TIRUPATI
3. BESANT THEOSOPHICAL COLLEGE, CHITTOOR
4. Sri Venkateswara Agricultural College
Tirupati, Andhra Pradesh
5. Acharya N. G. Ranga Agricultural University
Guntur, Andhra Pradesh
6. Agricultural College Bapatla
Bapatla, Andhra Pradesh

Dear aspirant,
Yes there are private institution which have agriculture engineering as their subject.https://www.google.com/url?sa=t&source=web&rct=j&url=https://engineering.careers360.com/colleges/list-of-agricultural-engineering-colleges-in-andhra-pradesh&ved=2ahUKEwjijo6jv8fiAhX-6nMBHWpMB2IQFjAEegQIBBAB&usg=AOvVaw0HqH4zGh3TvfE_CoDvN5a6
You can check this link for the College information.

Hi Karthik !
1.ABR College of Engineering and Technology
2.College of Agricultural Engineering - Madakasira
3.College of Agricultural Engineering - Sangareddy
4.KLR College of Engineering and Technology
5.Mother Theressa College of Engineering and Technology
6.Anu Bose Institute of Technology - ABIT
7.Avanthi Institute of Engineering and Technology - AIET
8.Narayana Engineering and Technology Campus
9.Nova College of Engineering and Technology
10.Siddharth Institute of Engineering and Technology - SIETK
And there are also another college in AP.