How do I not claim a standard deduction since I am a dependent and someone else will be claiming me?

You get a standard deduction whether you are claimed or not. What you don't get is your personal exemption, to make sure of that, in the Personal Info area when you are entering your personal information there is a box to check that says that you can be claimed on someone else's tax return.

It was marked that someone else can claim me.  Now mom is not able to claim the dependent deduction.  How can this be corrected via online amended filing?

Stick with your other post.  We don't know why it's not letting her claim you.  Your return is ok and right.  Is she filing a Joint return or did your father also claim you?