I have ipod nano 3rd generation. Is there a bluetooth adapter to use wireless headphones

There are third-party products for this purpose. There are two types. One type connects to the headphones jack. This type is for any device that has audio output from a standard headphones jack. For example

https://www.amazon.com/Bluetooth-Transmitter-Receiver-TROND-Wireless/dp/B01B4W40 VC

The other type connects to the iPod's dock connector. For example

https://www.amazon.com/KOKKIA-Transmitter-authentication-capabilities-generation /dp/B004SH40BQ

I have not personally used these types of products.