It would affect a lot of things but not the renewal. If made, the next inquiry before the claim sticks forever making you inadmissible and ineligible for naturalization with no waiver available, is whether it was a knowingly made claim and if not, whether you officially retracted it the second you figure out you made it.
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Have an immigration attorney file a FOIA request for the copy of your entire file with each CBP and USCIS (needs to file 2 FOIAs).
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As mentioned FOIA Requests can help. Also, your own memory. Why do you believe you made a false claim. A consultation with an immigration attorney may help you figure out if you did or not.
As the others stated, the FOIA requests are a good start. One thing that often shows up in the category is when someone gets their Driver's License and accidentally or unknowingly registers to vote. If this is so, you need to immediately get your name off of the voter registration rolls.
FOIA request generally filed to get information with specific agencies. You would need to recall where you could have made such claims. An error might be excused if properly argued, but a deliberate/misleading claim could result in loosing all immigration benefits. Proceed through an attorney, if such possibility exists.