What drug is in Percocet that is in common with gabapentin?

They are in different drug classes completely and do not share any common active ingredients:

Percocet (acetaminophen-oxycodone) belongs to the drug class of narcotic analgesics combination.

Gabapentin belongs to the drug class of Gamma-aminobutyric acid analogs.

Click on the link in order to access a full comparison between both medications:

https://www.drugs.com/compare/gabapentin-vs-percocet

Interactions between your drugs
Major
oxyCODONE gabapentin
Applies to: Percocet (acetaminophen / oxycodone) and gabapentin

Using narcotic pain or cough medications together with other medications that also cause central nervous system depression such as gabapentin can lead to serious side effects including respiratory distress, coma, and even death. Talk to your doctor if you have any questions or concerns. Your doctor may be able to prescribe alternatives that do not interact, or you may need a dose adjustment or more frequent monitoring to safely use both medications. Do not drink alcohol or self-medicate with these medications without your doctor's approval, and do not exceed the doses or frequency and duration of use prescribed by your doctor. Also, because these medications may cause dizziness, drowsiness, difficulty concentrating, and impairment in judgment, reaction speed and motor coordination, you should avoid driving or operating hazardous machinery until you know how they affect you. It is important to tell your doctor about all other medications you use, including vitamins and herbs. Do not stop using any medications without first talking to your doctor.

Source:
https://www.drugs.com/drug-interactions/gabapentin-with-percocet-1147-0-72-1135.html