Bitbns is currently the best exchange in India at the moments. They offer lots of coins for trading and withdrawal options.
This is peer to peer exchange, you can deposit money in spite of RBI ban.this is secure and trustworthy....I am using it...so you can go with this....
You can also try coincrunch...
Can you with draw ETH coins in bitdns even without verification? I think verification is for INR only.