Nope. Or at least, there’s very little information about the Moon Kingdom in general, and I suspect it is deliberate that Princess Serenity does not have a father. Note that Usagi Tsukino (who is not the same person as Princess Serenity, remember, just her reincarnation) does have a father – Kenji Tsukino. And yes, he’s her actual biological father.
The traditional rules of life and death don’t apply to the citizens of the Silver Millennium, and that includes reproduction. We know that because of the powers of the Silver Crystal, the Silver Millennium’s citizens have extended lifespans of around 1,000 years. Small Lady appears to be unusual in that we know who both her parents are, but we also know for sure that she is the first to be the heir to both the Moon Kingdom and Earth Kingdom. There are a lot of things about both kingdoms that we never know about. We don’t know if Queen Serenity was the first of the Moon Matriarchy, how long she’d been reigning for, when Princess Serenity was expected to take her place as ruler, etc. All we know about the Earth Kingdom is that Prince Endymion was their Prince, and that the citizens of the Earth Kingdom were not long-lived like the Moon Kingdom’s residents were. But we don’t know if Endymion was the Crown Prince or the ruler or what. We get a bit more information in the manga than we do in the anime, but there are still more questions than answers. All I can offer is my own theory.
Queen Serenity describes herself in the manga as an incarnation of the Greek Goddess of the Moon, Selene. Miss Dream’s translation has her saying that the people of Earth refer to her using the name “Selene.” The “Serenity” name is a pun combining both “Selene” and the “Sea of Serenity,” alternately known as “Mare Serenitatis,” a significant lunar landmark. In Greek Mythology, Selene fell in love with a mortal man named Endymion, who is alternately described as either a shepherd or astronomer. At some point, knowing that she is immortal and her lover is not, Selene asks Zeus to grant her wish that Endymion would be put in an eternal sleep and would never leave her (the specific reason why differs on the poet chronicling the myth). The myth of Selene is split between Queen Serenity and her daughter. Note that Selene was a Titan, and her position as Moon Goddess was eventually replaced by Artemis, much like how Helios as God of the Sun was eventually supplanted by Apollo.
Queen Serenity describing herself as an “incarnation” is quite important, as the word has quite a few significant meanings. It could that she is (or was) a living being embodying a deity or spirit, or that she is the goddess in human form. In Christianity, Jesus is referred to as the “Incarnation,” meaning that He is both God and Man. She could also literally be Selene from the era of Ancient Greece, since we don’t actually know when the Moon Kingdom took place. Silver Millennium is the name of the political entity ruled by the Serenities, which applies to both the Moon Kingdom of the past and Crystal Tokyo of the future. It’s a confusing name for sure, and it doesn’t help that the 90s English dub is the only version of the series that explicitly said that the Moon Kingdom was 1,000 years ago. My best guess as to what the name means is that it is referring to how the “Silver” Crystal extends the lives of its people to roughly a “Millennium.” So what does all this mean? That Queen Serenity, as a physical humanoid embodiment of Selene, has all the powers of the Greek Gods. And the Greek Gods can thwart the rules of reproduction all they like.
You are likely familiar with Athena, the Greek Goddess of Wisdom (and a whole bunch of other things). Here’s a quick summary based on her Wikipedia article: Although conceived in the usual way with deities Zeus and Metis as her parents (Zeus basically slept his way across the entirety of Greece), Metis was prophesied to bear children more powerful than their sire, even Zeus. As Zeus only became the leader of the Gods because he supplanted his own father Cronus, who overthrew HIS father Uranus (talk about a dysfunctional family), he was understandably fearful of this. His “brilliant” solution was to swallow Metis whole, but she had already conceived. Time passes and he gets the world’s worst headache, another God (none of the poets agreed on which) cleaves his head open with an axe, and out pops Athena, fully grown and armed. Hera, Zeus’ ever-suffering and ever-jealous wife, conceived and bore Hephaestus (God of Blacksmiths and Craftsmen) by herself in an attempt at revenge, but he was born misshapen and with a lame foot.
Ancient Greece was a rather misogynistic society (look at how negatively Hera was portrayed for being jealous over and suspicious of a husband who cheated on her constantly), so it is possible to interpret these myths as trying to downplay the role and necessity of females for reproduction. However, Sailor Moon was deliberately intended as a feminist series, so through Queen Serenity we have a possible example of a woman’s asexual reproduction that not only turned out perfectly, but continues the line of a powerful matriarchy. During the Dream arc of the manga, we see a flashback of what appears to be Princess Serenity’s christening, so we know at least that Princess Serenity wasn’t born fully formed like Athena was. We also know that the Silver Crystal has near-infinite powers, which specialize in healing, reincarnation, and resurrection. So it’s not too much of a stretch that the Crystal could have life-creating powers as well.
I suspect that one reason why fraternization between the Moon Kingdom and Earth Kingdom’s citizens was forbidden was because of their vastly different lifespans. What would happen if a Moon Kingdom citizen had a child with an Earth Kingdom citizen? How long would that child live? Where would that child reside? When it comes to Princess Serenity, we don’t actually know what Queen Serenity’s plans for her were, beyond instructing the Guardian Senshi to protect her at all costs. What if, initially, she was supposed to continue the line solely using the Silver Crystal like her mother did? We never get to know this, as in a scene directly inspired by Sleeping Beauty, Nehelenia crashes Princess Serenity’s christening party and eventually curses that Princess Serenity will die before taking the throne.
As we find out later, Neo-Queen Serenity is able to use the Silver Crystal to extend King Endymion’s lifespan, and their daughter Small Lady also has a very long lifespan. I think that part of the reason this worked out is that Neo-Queen Serenity is not a Moon Kingdom resident now, she is from Earth like her husband. Unlike Queen Serenity, Usagi is NOT an incarnation of Selene, she’s a “normal” teenage girl. If she had been a reincarnation of Selene, Queen Serenity would have told her so – she only describes HERSELF as the Goddess. So Small Lady is definitely the first of her kind, but notice that any Earth powers she would have had don’t manifest themselves – she explicitly is meant to continue the Silver Millennium matriarchy.
The theory that Queen Serenity created Princess Serenity asexually thanks to the power of the Silver Crystal is also bolstered by a scene late in the manga in which we see a flashback of Queen Serenity visiting the Galaxy Cauldron, the place in which all stars are born. The guardian of the Cauldron, Guardian Cosmos, tells Usagi that long ago, a person just like her (shown to be Queen Serenity) came to the Cauldron clutching a fledgling star that is heavily implied to have become Princess Serenity. Naoko Takeuchi prefers to tell her story symbolically which is why this theory is only heavily implied rather than directly stated.
It is probably deliberate that “Does Princess Serenity have a father?” has no definite answer, only theories. It certainly wouldn’t be anti-canonical to invent a husband/father in fanfiction, unlike how a Sailor Earth OC ignores that Mamoru is canonically the holder of the Sailor Crystal for Earth. But I think my theory of a combination of Queen Serenity’s Greek God powers/origin and the Silver Crystal’s powers facilitating Princess Serenity’s birth makes sense. It’s hardly an untapped concept; for example, Anakin Skywalker was conceived asexually of The Force. My hope is that someday we’ll get more information and more answers about the Silver Millennium society. It’s a fascinating concept full of untapped potential.
Manga scan by Miss Dream and coloured by me.