@Aman Soni , I have heard that HDFC provides netbanking for minors as well.
Also, if you personally hold account with Axis bank you can open minor account there and through your login credentials you can apply for your child.
Also, select his/her account to block funds to avoid third party rejection.
For broker - I think Prostocks is the only one which allows selling IPO's from minor's account.
I'm also think of opening Axis Bank and Prostocks account for my son.