You can appear for JEE Mains/Advanced for all the governmental institutions. An exam specific to Andhra Pradesh is EAMCET, which does not offer the variety of B.Tech courses you will get from other papers. Other private exams include BITSAT, VITEEE, SRMJEE. Some private colleges even accept your JEE Mains scores for admissions.

To take admission in top engineering colleges you have to appear for the entrance exam. Below are the entrance exams in which you can appear

1- JEE (Main+Advanced)- To take admission in NITs/IITs/IIITs and CFTIs.
2- EAMCET- To take admission in government colleges of Andhra Pradesh
3- BITSAT
4- SRMJEE
5- VITEEE
6- Manipal
7- Amrita

You can check the complete details of the entrance exams from the given below link
https://engineering.careers360.com/exams

Good Luck!!