The story of Ash Ketchum's family is one of the longest running mysteries in the series. Even though his mother is an important character, we still know nothing about his father, aside from a few references in the early parts of the anime.
The mystery of Ash's father was never resolved in the final season of the Pokemon anime, and now the story has been continued by Pokemon Horizons, with a new cast of characters residing in the Paldea region.
The main characters in Pokemon Horizons are Riko and Roy. Fans have speculated that Riko has a connection to Ash, hoping to connect the main characters of the two series. But is there any evidence of a family relationship between Ash Ketchum and Riko?
There is no evidence that Ash Ketchum and Riko are related. Riko's parents have both been revealed, so we know it can't be a time-travel situation where an older Ash Ketchum is her father.
The door for a connection between the two is still open as Riko and Ash may have the same father. Riko's father, Alex, has appeared in the series. However, despite Alex's physical similarities, there is no confirmation of a connection between the two.
There's a bit more evidence that Roy, Pokemon Horizons' other main character, is related to Ash, as it's been confirmed that he's from the Kanto region. However, nothing else binds them together other than their aesthetic and personality similarities.
A crossover between Ash Ketchum and the heroes of Pokemon Horizons seems likely and could also be the plot of an upcoming Pokemon movie. If there are any connections between these three, they will be revealed. But until then, there has been no confirmation that any of the main characters in the Pokemon anime are related.