Yes u can join in engineering in ap without writing JEE MAINS or Ap Eamcet.

But its better to write either JEE MAINS or Eamcet. I will list some the benefits of JEE MAINS and Eamcet.

Benefits for JEE MAINS :

1.Firstly, clearing the JEE MAIN xam will help a candidate qualify to write he exam of JEE Advanced. If a student cracks the competition on both levels, he/she can get entry into the top-most colleges across the country for any major course such as B. Tech, B. Arch.

2. Helps in getting seats at the top colleges.

3. Prepares you for the real world and gives you an insight into the competition.

4. Learn how to manage time efficiently.

5. You can go for higher studies.

6. If you score more percentile then you will have chance to get into NIT'S and IIT'S.

Benefits for Eamcet :

1.Engineering Agricultural and Medical Common Entrance Test, commonly called as Eamcet, is an entrance examination held separately in the Indian Telugu States of Andhra Pradesh and Telangana for admission into various colleges across both the states in the streams of Engineering, Medicine and Agriculture.

2. A good rank in Eamcet will get you a seat in a good college in your chosen professional degree.

Hope this will be helpful for you.

ALL THE BEST.