X-23 first appeared back in 2003 with the 11th episode of season 3 to X-Men Evolution. The episode is titled "X-23." It aired originally on August 2nd. Here is that episode.
Her story received a follow up in the series during season 4 with episode 3. This episode is called "Target X" and aired on September 13th, 2003. You can watch it below.
As you can see, many elements of the episodes were carried over to the 616 universe stories along with some names. Most of it was swapped around though with X-23 herself being altered to fit much better within the confines of 616 Marvel and present even more complexities than her initial tv animation appearances could allow. This included correcting a few minor story issues like how X-Men Evolution had said her bones were coated with adamantium via the same process as Wolverine.
My apologies if you are of a region that cannot watch how these are presented. That is outside my control due to the rights nature involved of bringing these episodes to you through the blog via the appropriate channels.