I had custody of my daughter from the ages of 7 to 13 I never took a child support case out on her mother while she was living with me can I ask the courts for child support back pay from the mother now even though my daughter currently lives with her mother or it to late?

It will depend on where you live, what county ( we are a international site) and if the US, what state ( laws vary by state)

In a few states you can file for support for the past, in many states no you can't.

Also during those years of 7 though 13, who had legal custody.

And why did legal custody change? ( or at least physical) I am assuming mother has legal custody now.

I wouldn't bother asking for it unless there is a dispute over it as in the mother trying to get support at this time. Having the child from 7-13 makes 6 years. And if the mother should have the child for the next 6 years then it is a form of split custody. You can argue it out in that way so no current support is due.