Hello,
Based on your rank in JEE Mains and also as you are from EWS category, you have quite some chances of getting a seat in government engineering colleges like NITs IIITs and GFTIs. You might not get core branches but you will surely get other branches. You should definitely register for JOSAA counseling through JEE Mains.
Please visit this link for JEE Mains college predictor

Also, you have decent rank in both AP EAMCET and TS EAMCET, so you might as well get good colleges through them as well. So please go for the counselling of both TS EAMCET and AP EAMCET.
Your hard work has bring you good ranks in three exams. So please go for all three counseling and choose the best college you get and the branch of your choice.

Please visit the below links for college predictor
AP EAMCET college predictor

TS EAMCET college predictor

All the best

Hope it helps

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