It sounds more as if you want to know what happens if this other person commits perjury while testifying at a support hearing. These cases are notoriously tough to get prosecuted. First you would need for the hearing to be recorded by a Court Reporter and transcribed to get anyone in law enforcement's interest. If you or your attorney catches the other person in a lie often the best result you will see is a ruling in your favor and the Court looking upon the other person with a suspicious eye in the future.
My guess is that if the other person were so prosecuted they would probably see probation.