I have been dealing with Content ID false claims for three years across my channel and have had to dispute over 40 of them. Let me walk you through the process since it is not well documented anywhere.
When you receive a Content ID claim, you have three options in YouTube Studio: dispute the claim, trim out the claimed segment, or replace the audio. For a false claim, always dispute. You select the reason (I own the rights, fair use, the content is in the public domain, etc.) and provide a brief explanation. The claimant then has 30 days to respond. If they do not respond, the claim is released automatically.
If the claimant rejects your dispute, you can appeal. This is where it gets serious because a rejected appeal can result in a copyright strike. However, if you are confident the claim is false, the appeal is your best option. After you appeal, the claimant has 30 days to either release the claim or file a formal DMCA takedown. Most false claimants will not file a DMCA takedown because doing so under false pretenses carries legal liability including perjury penalties under 17 USC 512(f).
If you are losing significant revenue to false claims, document the revenue impact through your YouTube Analytics. This data can be critical if you need to pursue a 512(f) misrepresentation claim. Several YouTubers have successfully sued false claimants and recovered damages plus attorney fees. The Lenz v. Universal case established that copyright holders must consider fair use before issuing takedowns.
One more tip: if you are using royalty-free music or stock footage, always keep your purchase receipts and license agreements. These are your strongest evidence when disputing Content ID claims on licensed content.