As a practical matter, there is really nothing you can do to stop a noncustodial father from filing motions to modify custody until the child reaches the age of majority. Most judges are reluctant to find one side lied in a motion; the judge is more likely to conclude one side is simply not credible or reliable. It takes a long history of abusive motions for a court to pre-emptively forbid a litigant from filing motions, and such pre-emptive orders are extremely rare.
The way to make is stop is to hire an attorney, have the attorney prepare a polite and respectful opposition, and then if you win the motion to move the court to have the noncustodial father pay for your attorney's fees. If you win these motions, after time it will simply become too expensive for him to continue filing motions and he will stop for financial reasons.
Most court's will not consider two motions to be abusive; there has to be a longer track record for the court to reach that conclusion.
If the non-custodial father is truly telling lies, then fully litigating the matter to show the judge how he is lying will go a long ways to persuading the judge to take action. However, no judge will prohibit the noncustodial father from filing a motion simply because you think the father is lying.
Hope this helps.
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