In the chronology, the Peking episode is the last of the ten hours to feature Corey Carrier as Younger Indy, but I think that it might have been the third one produced, and it also might have been planned as the third one with this cast to air.
When ABC first gave The Young Indiana Jones Chronicles its six week run in the spring of 1992, they showed the Curse of the Jackal movie (“Egypt, 1908” and “Mexico, 1916”) and five one-hour installments. Merchandising takes a little while to get circulating, and it wasn’t until the summer that we started seeing tie-in material. There were chapter books and coloring books, sticker albums and magazines, and trading cards issued by a company called Pro Set. These were very interesting: the cards told the storyline of the episodes of the first season, except they added the Peking adventure, which was written by Rosemary Anne Sisson, before the show’s closing two-parter.
Did ABC originally plan to show six episodes after the movie? We can only speculate, but ever since I saw those cards, I have believed that they intended to show this story on April 1 1992, with the German East Africa/Congo 1916/17 episodes on April 8 and 15. The network got cold feet after the poor critical reception to the first half of Jackal, and quietly moved this one into limbo. It finally aired in June 1993, after the show had been canceled.
It’s really too bad that the Younger Indy stories weren’t better received, but they’re still not being very well received in our house today. This isn’t a very talky episode, but it’s more of a drama for grownups. Indy gets incredibly sick while the family is miles from a city, and it will take several days for the nearest American-trained doctor to be brought to the house where they’ve found refuge. The only real drama comes from waiting for Indy’s mother to swallow her pride and agree that a local doctor can treat him with acupuncture.
All ends well, of course, but our son seems pretty glad that they’ve ended, period. I’ve assured him that the rest of the series would have a little more action in each hour. Not every one of them, mind you, but we’ve got some spies and criminals and enemy soldiers for an older Indy to tangle with starting about six years after the family left China…
Fire Breathing Dimetrodon Time 
That’s Ping Wu with Young Indy in the picture you’ve chosen. He is in every American TV show these days.
I just looked at his IMDB page and you’re right, especially on all the crime shows on CBS.