At the very least, to fight false allegations of abuse you need compentent legal counsel. You'll need to do your best to prove that the allegations are unfounded, malicious, or incapable of having occurred.
Unfounded allegations are allegations where there is no supporting proof and no evidence that to show that the abuse actually occurred.
Malicious allegation are frequently made in the context of heated divorce and custody battles. They are suspicious by their very timing and may be obvious to the trained professional or the informed layman.
Allegations that are incapable of having occurred are those where you can prove you had no physical access to the child (such as being out of town or in the hospital on the dates when the abuse is alleged to have occurred), or other factors that would make it an impossibility for you to have committed the alleged abuse.