Can they charge me the child support from that day back started 12 03 2003. Till 02 24. 2009

As I understand it, you were sued for child support, but the case was dismissed. Apparently they have re-filed, and you are asking whether they can seek child support for the period from 2003 through a date in 2009.

It depends on what state or country this is. The statute of limitations may have expired. Also, in some states, retroactive child support isn't allowed anyway. Apparently OCSE is claiming this to recoup some assistance they paid to the custodial parent; in that case a retroactivity prohibition might not apply.

Was a child support order (either as part of a divorce or otherwise) previously entered?

The courts dismissed my child support case in 2009. For want of prosecution without prejudice
Neither party done any thing on the case for year half so court dismissedn 2012 I was given class b felony for nonsupport by same court for 40.000 back child support am incarcerated at this time over it

There is two issues, civil payment of child support.
And criminal charges.

What was dismissed, criminal charges?
If there was child support, not paid, and there is a court order for that payment, depending on where you live. They can collect that.

There are issues about criminal charges, since if you are not current, then it is not a one time issue, but would look at the point, support no longer was due. (again depends on local laws.

The courts dismissed my child support case in 2009. For want of prosecution without prejudice
Neither party done any thing on the case for year half so court dismissedn 2012 I was given class b felony for nonsupport by same court for 40.000 back child support am incarcerated at this time over it

So the cases were dismissed twice, once in 2009 and again in 2012? As others have noted, it is important that you be clear: were these civil cases or criminal cases?

So now you have been convicted of a felony, and are serving time, for failure to pay $40 in back child support. Seems a bit extreme, but what is it you want to know about that?

I'm guessing here, but it could be that the earlier dismissed cases were civil cases (which would make sense if pursued by OCSE on behalf of the custodian). If so, the prior dismissals would be no bar to your more recent criminal prosecution.

It's interesting, by the way, that you are able to access the Internet while in jail or prison. I didn't know that was possible.

So the cases were dismissed twice, once in 2009 and again in 2012? As others have noted, it is important that you be clear: were these civil cases or criminal cases?

So now you have been convicted of a felony, and are serving time, for failure to pay $40 in back child support. Seems a bit extreme, but what is it you want to know about that?

I'm guessing here, but it could be that the earlier dismissed cases were civil cases (which would make sense if pursued by OCSE on behalf of the custodian). If so, the prior dismissals would be no bar to your more recent criminal prosecution.

It's interesting, by the way, that you are able to access the Internet while in jail or prison. I didn't know that was possible.

I think the OP meant for the arrears to be $40,000. Not $40.

We do need clarity as to what the case was about as far as civil or criminal inorder to give a decent answer.