According to Evelyn, there was no father.
But Samara's biological father is apparently a sea demon that would have come "from the waters of the world beyond this one". It's very possible that Samara inherited her powers from him.
In "the ring 2", Evelyn told to Rachel that the nuns allowed "the dead to get inside Samara" when they stop her effort to drown the baby. If he is related with this fact, it's unknown.
Trivia
Maybe Samara´s biological father could have some similar characteristics to the mythological creature "Leviathan". Both are sea demons with some kind of connection with the "world of the dead". Originally God produced a male and a female leviathan, however their children should destroy the world; then God killed the female, leaving the male alone and revolted. Leviathan lives in the depths of the ocean, where he serve as the gatekeeper of the underworld. In Demonology, he is one of the seven princes of Hell. Some myths think that the sea is the "incarnation" of Leviathan.