Been divorced since 96 it has recently come to light that the ex has told the youngest child she is not mine can I petition the court for a dna test since she seems to already know that the child is not mine if she has told the child I am not her father... I have ask her for a private one she told me will have to take her to court
I know from what I have read there have been a couple cases in Ohio where this has been done

...i have ask her for a private one she told me will have to take her to court ...

And what is your question?

Do you have shared custody or visitation? What's to stop you from simply asking your child to give you a cheek swab? Send it in along with one of yours, and you can get the answer, quick and easy.

You do know that such a "private one" is not admissible in court?

As AK pointed out, if you have joint legal custody and visitation, you don't have to ask the mother's permission to do a cheek swab.

However, if the child was born during your marriage, then you are the legal father. The time may have expired on when you could challenge that, even if she is not your biological child.

5101:12-40-05 Determination of the existence or non-existence of a father and child relationship.
(5) “Disestablish paternity” means to attempt to overturn or reverse a final and enforceable determination of paternity.
(6) A “final and enforceable determination of paternity” exists when:
(a) In accordance with section 3111.25 of the Revised Code, the mother and father signed a JFS 07038, “Acknowledgment of Paternity” (rev. 12/2006), and neither the mother nor the father brought an action under section 3111.27 of the Revised Code within sixty days of the signing to request the JFS 07038 be rescinded, and the JFS 07038 has been determined to be completed correctly;
(b) In accordance with section 3111.49 of the Revised Code, a child support enforcement agency (CSEA) issued a JFS 07774, “CSEA Administrative Order – Establishment of Paternity” (rev. 11/2001), or JFS 07771, “CSEA Administrative Order – Non-existence of Child-Parent Relationship”
(c) A court issued an order determining that the man is the father of the child or that the child was born as a product of the marriage and neither party to the order objected to the order

(2) (E) Pursuant to section 3111.05 of the Revised Code, an action to determine the existence or non-existence of a father and child relationship may be brought up to and including the child’s twenty-third birthday.
3111.03 Presumption of paternity.
A) A man is presumed to be the natural father of a child under any of the following circumstances:

(1) The man and the child’s mother are or have been married to each other, and the child is born during the marriage or is born within three hundred days after the marriage is terminated by death, annulment, divorce, or dissolution or after the man and the child’s mother separate pursuant to a separation agreement.
(3) An acknowledgment of paternity has been filed pursuant to section 3111.23 or former section 5101.314 of the Revised Code and has not become final under former section 3111.211 or 5101.314 or section 2151.232, 3111.25, or 3111.821 of the Revised Code.

(B) A presumption that arises under this section can only be rebutted by clear and convincing evidence that includes the results of genetic testing

3111.05 Statute of limitations.

An action to determine the existence or nonexistence of the father and child relationship may not be brought later than five years after the child reaches the age of eighteen. Neither section 3111.04 of the Revised Code nor this section extends the time within which a right of inheritance or a right to a succession may be asserted beyond the time provided by Chapter 2105. 2107. 2113. 2117. or 2123. Of the Revised Code.

Ohio has laws allowing ex-husbands to overturn a child-support order when deception or fraud by an ex-wife is discovered. By contrast, most other states set a one- to four-year deadline for fathers to file lawsuits challenging paternity determinations.

Following the uproar over the treatment of Dennis Caron, Ohio passed a law requiring relief from child support orders at any time upon proof of biological exclusion.
The right of action is limited to the men subject to the orders. The evidence must be in the form of a genetic test showing zero probability that the man is the father of the child. A marriage to the mother or any admission or acknowledgment of paternity is irrelevant if the man was not aware of his non-paternity at the time.
/Disestablishment Suits.What Hath Science Wrought?Mary R. Anderlik, J.D. Ph.D./

The ex will not allow visitation that has always been a struggle I have tried on several occasions I can not afford every time she says no to go back and get a lawyer and she says no all the time... the child will not even acknowledge me in public... and refers to me by my first name and not dad... I am basically the financial support and that is all I am allowed to be... I would have done the cheek swab when she was younger if I had known... know all I can do is ask the court to help me and hope they do I am not behind on my support

I know that custodial parents will abuse the law. But if were given a visitation order as part of the divorce, I don't understand how she can refuse visitation. You don't need a lawyer to ask the court to cite her for contempt of court.

However its probably too late for you now. The best you can hope for is to contact the children once they turn 18 and prove to them that you tried to see them but their mother prevented it.

Back to your question. According to the law GV70 cited, you have until she turns 23 to file for an adjudication of your paternity.