During the 400 years of his life, John Amsterdam (under all of his aliases) had 63 children. So we could make the claim that he's related to a lot of previously established TV characters. And unlike the protagonist Cormac O'Connor in Pete Hamill's novel "Forever" which had a similar theme, John could leave Manhattan. So these children could be spread all over Toobworld.
And they don't have to be directly father and son or daughter either. We could suggest that somewhere farther back in the family tree, John sowed the seed that would eventually lead to the TV character in question.
And I have the perfect first candidate for this:
I wouldn't stretch the genealogical distance between John Amsterdam and Fox Mulder too far. I think we'd be safe in making the claim that John was Fox's great grandfather, perhaps even his grandfather on his mother's side.
But the resemblance is close enough there to make the claim that they're related; much better in fact than in some established cases in TV - like Jerry Stiller and Leah Remini!
[The picture of Nicolaj Coster-Waldau is one of the basic photos for 'New Amsterdam' publicity shots. So I knew just where to look to get a similar shot for David Duchovny - the "Leonard Betts" episode of 'The X-Files'!]