Hey Anushka, you can give both exams. 
As AEEE is an entrance exam for Amrita Vishwa Vidyapeetham only so you won't get benefits of rank in this exam in other colleges so you must give both the exam.

But you can apply for admission in the Institute with either Jee mains rank or AEEE rank.

Applying from both exams simultaneously is not allowed.

It will be better to apply from Jee mains if you manage to get a good percentile which is enough to get admission in good branch.

And if percentile is not that good then AEEE is the only option left.

Hope you will understand.