People have speculated that Fantastic Beasts will tie in to Voldemort's birth, due to the fact first movie takes place in 1926. Voldemort (Tom Riddle) is born of Merope Gaunt on December 31st 1926. A poster seen in the first Fantastic Beasts movie speaks of a circus called the Circus Arcanus moving from New York to Europe on December 13th 1926. The last trailer for the new Fantastic Beasts movie confirms that the 'snake girl' who is part of the circus is Nagini, a maledictus who will go on to become Voldemort's pet snake. This is a secret Rowling says she has carried for 20 years. So we have Nagini in the right location and the right time, but that is no confirmation that Nagini is Merope Gaunt.
In Half-Blood Prince, we find out from Mrs. Cole that Merope arrived at Wool's orphanage, gave birth to Tom Riddle, and died soon after, though I believe Merope faked her own death. Cole says:
'I remember she said to me 'I hope he looks like his papa', and I won't lie she was right to hope it, because she was no beauty — and then she told me he was to be named Tom, for his father, and Marvolo, for her father — yes, I know, funny name, isn't it? We wondered whether she came from a circus'
So this could be a coincidence, but it seems Rowling may already have had the idea that Merope/Nagini was part of the Circus Arcanus. Perhaps Merope was looking ugly due to her upcoming permanent transformation into a snake. Perhaps Merope gave her child to an orphanage before faking her own death and running away so she would not harm her child after her snake transformation. The Gaunts after all are desceneded from Salazar Slytherin - what better family to carry a snake curse?
If this were true, and Voldemort was the child of the maledictus Nagini, it would explain Nagini's maternal relationship with Voldemort in the books. If the two were able to communicate via parseltongue, this theory would explain why Voldemort is so fond of Nagini, entrusting her to become a Horcrux. Voldemort drinks Nagini's venom to regain strength in his baby-form in Goblet of Fire, an obvious parallel to mother's milk. It may even explain why Voldemort develops snake-like characteristics.