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No, you cannot fight this and win.
The state of Texas allows employers to deduct according to their payment schedule. If he gets paid biweekly, that's how they'll withhold. Although your order states 1st of the month, the OAG will only care and enforce the order if he doesn't finish paying within the month. There may have also been a "withholding" order sent to his employer that outlined that they could withhold monthly, bi weekly, weekly, etc. That order would give his employer the ability to do that.
Additionally, employers in Texas can only take up to 50% of an employee's paycheck each time, so if his monthly child support is more than half of his paycheck his employer would be breaking the law to take all of it out of his first paycheck.
The only way to avoid this is if he pays directly to the OAG State Disbursement Unit. Most custodial parents prefer that the child support be deducted from the paycheck because it is more certain and you are more likely to obtain it in a timely manner.
I understand that this information may frustrate you, but lawyers must tell the facts as they are, not as people wish they were.