No direct-relation sequel to original Black Jack. Black Jack attempts to find out the conspiracy, of why he was involved in the bombfield accident that killed his mother, while he uncovers secrets of Organization and Project "Noir", which, his father and other famous doctors were involved in...

Black Jack is an "unregistered" doctor with a clouded, mysterious past. He works with his little assistant Pinoko (who has a massive crush on the doctor), dealing with medical cases not very well known, which can be strange, dangerous, or not known at all. But he is a genius, and can save almost any of his patients' life (as long as they have the money for it, that is), and is known to many around the world, especially to those of medicine and science. He's a man of science himself, and does not believe much until he has seen it, yet it is many times he is surprised by love and nature often overpowering the science he bases his life in. 
(Source: Anime News Network)

Among adult readers in Japan Black Jack is Osamu Tezuka’s most popular achievement, and perhaps the most close to the creator’s heart, as Tezuka considered entering the medical field—majoring in medicine in college—before devoting his life to comics. Black Jack is a genius surgeon who never acquired his license due to his clashes with the medical establishment. He is hired out by anyone willing to pay his exorbitant rates and is perceived as a heartless rogue because of his enigmatic nature and antisocial manner. But as readers will soon discover, that is not the whole story.
 
(Source: Kodansha USA)
 Note: Won the 1st Kodansha Manga Award in the Shounen category in 1977.

This was originally from the Black Jack (2004), but weren't aired then, only later. There are two episodes in this: 
"The Dog Thief" 
"Kamaitachi in the Woodlands"

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