Ethernet - TeensyUser/doc GitHub Wiki
Teensy supports both wired and wireless SPI-based Ethernet solutions like Wiznet W5500 (wired) using Arduino's Ethernet API and ESP8266 (wifi). The Tennsy 3.5/3.6 and Teensy 4.1 also support native wired Ethernet.
T3.5/3.6 native Ethernet
In 2016, a few Ethernet shields were provided for the T3.5/3.6 beta testing, see T3.5/3.6 Ethernet tests using lwIP.
T4.1 native Ethernet
In 2020, an Ethernet adapter was provided for the Teensy 4.1, see T4.1 Ethernet testing.
This PCB from OSHpark allows you to connect the ethernet pins on the Teensy 4.1 to an ethernet cable, via a 2mm pitch breakout cable, buy Teensy Ethernet kit.