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 Bloods and Red Bloods, vampires and humans. Despite their differences, these two races once fought together in a crusade against a formidable foe. A decade later, the vampire war hero Jirou Mochizuki, known as the Silver Blade, travels with his younger brother Kotarou to the Special Zone—a safe haven where vampires and humans live in harmony. However, their journey is suddenly faced with danger when a conflict erupts between vampire migrants and human forces from the Special Zone. With the rise of a developing conspiracy from an old enemy, Jirou will need the help of his new ally, Mimiko Compromiser Katsuragi, as well as the power of his ancient bloodline to protect what he treasures the most.

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

Salaryman Rokurou Okajima spends his days trying to climb his company's corporate ladder, until one day when a business negotiation in Thailand goes awry. During the botched deal, he falls hostage to the Lagoon Company—a band of ruthless pirate mercenaries. Left to the whims of his captors after his managers refuse to pay his ransom, Rokurou does the unthinkable: instead of begging for his life, he joins the very crew who kidnapped him. Now a member of the group, Rokurou must adjust to his new residence in the dissolute hellscape known as Roanapur, a city where corruption and crime run rampant, and even the smallest slipup could cost him his life. If not for one of the many crime syndicates on the island, Rokurou also constantly finds himself at odds with his brash, gunslinging colleague, Revy. As Rokurou struggles to abandon his past—and with more than just the profits from the Lagoon Company's illegal trading on the line—he must quickly find the resolve to make tough decisions in high-stress situations while keeping his humanity intact.