No one in One Piece believes Weevil's claims of being the biological son of Whitebeard. But there is debate about it amongst us fans, one theory is that Weevil is a failed clone of Whitebeard.
This theory has been bolstered by Miss Buckin's claim that Vegapunk can prove that Weevil is related to Whitebeard.
It is heavily implied that Miss Buckin was a part of MADS. And she was in the Rock Pirates with Whitebeard. so could of taken a sample of his bloodline elements.
She herself was successfully cloned by MADS. One hole in the theory is that Weevil has a different blood type from Whitebeard but is the same as Miss Buckin.
I think Weevil is a male clone of Miss Buckin that was augmented with the bloodline elements of Whitebeard and Rocks D. Xebec.
With cloning becoming more prominent in the story there has been theories of Blackbeard being a clone of Rocks. Since he is Luffy's dark parallel I think he just has a similar personality. This wouldn't be the first time a character claiming Whitebeard as his father turned out to have an even more significant biological father.
The Seraphim are proof that clones can be spliced with other bloodline elements.
It was confirmed that their Lunarian genes came from the blood of King
Vegapunk has the ability to change the gender of clones.
Because of Weevil's proclaimed connection to Whitebeard and protecting his home town. I think the sphinxs from Sphinx Island are also foreshadowing that Weevil has several bloodline elements since they are chimeras.
Dream Koi from Wano ended up being foreshadowing that Kaido was a fish dragon zoan.
I think this will become significant in the story because it was hypothesize by Pythagoras that clones have the memories of the originals. So if my theory is true then Weevil has the memories of Rocks.