There is no such thing. When you’re using TTN’s community network then your gateway is “public” by definition.
Note that contact details and location might be hidden by an owner, but even then the gateway will just forward all LoRa packets it receives to the network it’s connected to, in this case TTN. TTN will ignore messages sent by devices from other networks, but all devices properly registered with TTN will see their data end up in their application, when received by a gateway that is registered with TTN.