I am trying to fight my exwife on areers, i had in my creed that if i have my son for 3/4 of the month i wouldnt owe child support. now she filled with the San Antonio Attn Gen for back areers. 40,000.00. i have evidence he was with me, round trip plane tickets, school records when he lived with me, my sons testomony. I have two questions. Is there a stature thats says i have to settle the areers case in a certain amount of time (i.e. before my son turns 20yrs of age, or in two years past his 18th birthday)? And second how can i fight this?

Given the wording of your first question I cannot tell whether you asking about the statute of limitations for the filing of past-due child support arrearages or whether you are asking how long you have to settle an arrearage matter once a suit has been filed against you or a default judgment has been obtained against you.
With that being said, assuming you are asking how long after the arrearage is incurred that a suit can be brought against you for the amount, the Texas Family Code states that a motion to render judgment for past-due child support arrearages must be filed no later than ten years after the date on which (i) the child becomes an adult or (ii) the support obligation terminates under the child support order. Tex. Fam. Code § 157.005. Thus, the court retains jurisdiction to reduce child support arrearages to a cumulative money judgment until ten years after either of the above occur.
However, if you were asking about the time limit you have to settle a pending arrearage matter or appeal a Judgment against you for child-support arrearages than that is a different matter. Under Texas law to reduce child-support arrearages to a cumulative money judgment a party must file a motion to confirm arrearages. Once the motion has been filed the matter will be set for hearing, and the responding party, which would be you in this matter, should receive a notice of the hearing.
At any time before the hearing you can file an Answer to the allegations. The hearing is your time to tell your side of the story. At the hearing you will be able to testify, present evidence, and call witnesses to support your understanding of the situation. I have not reviewed your specific Divorce Decree so I do not know whether the provision regarding child support payments when you have the child ¾ of the month is enforceable or not. If it is enforceable as written, then you would want to present this as evidence to the court. After hearing all of the evidence, the court will make a finding regarding the arrearages.
However, if a Default Judgment has already been obtained against you for the arrearages, then you only have a limited time to appeal the decision of the court. Generally, the court will lose power to hear your motion on the 31st day after the judgment is signed by the court. So if you wanted to appeal your arrearages judgment you would need to do so in most cases within that time frame.
Thank you for submitting your question for more information on this topic or to obtain legal advice on your specific situation please contact a Texas Attorney. Please be advised that my answering of this question does not constitute an attorney-client relationship.