There are many ways to go about this, but one of my personal opinions is that Palpatine is in fact Anakin’s father. Let me explain. In the Darth Plagueis novel by James Luceno, which is no longer canon, but still loved by fans. Plagueis and Palpatine were experimenting with the secrets of preserving life, and manipulating the force and the midichlorians to uncover the secret of prolonging their life indefinitely. This has been a goal of many Sith since the order’s inception. Due to Plagueis’ persistent manipulation of the force and midichlorians, the force itself answered back as a counter response to their experiments. That answer was Anakin. And thus Anakin was created by the force itself as an indirect result of the experiments. However I would like to counter this. If we take the Darth Plagueis novel as a sort of pseudo canon explanation, then that is what happened, but if we look at the films, and what George Lucas put in the films and what he was planning to put in the films, then we get possibly a different explanation.
We see in Revenge of the Sith, Palpatine explains to Anakin how Darth Plagueis was so powerful, he could influence the midichlorians to create life. As he explains this he looks at Anakin with a particular look, as if he was eluding to something. He looked at Anakin as if he was taking pride in his own creation. This is however only speculative, based on the framing of the scene and acting. I would like to further this however, with the fact that, from a filmmaking and story telling perspective, there is no point to have included that line in the film. If we never furthered that line later on in the film, and have only explored it in an unofficial (and fantastic) novel, then the line served no greater purpose. As Palpatine’s goal during the film, and in that scene was to explain to Anakin that there was a possibility that one could prevent someone from dying, knowing Anakin had turmoil and fear about losing Padme, and using that fear against him by offering a solution. That was the whole point to the scene, but the line about creating life, derails from that objective, and does not have any inherent value to Anakin, or the conversation. Thus I find it plausible that Palpatine was the one who created Anakin.
I would also like to add that, the novels were never considered canon by George Lucas, that they were side stories created that could exist alongside his stories, but he had complete control. And anything he decided to make, was canon. Such as the difference between Boba Fett’s original story in the novels, and the story of Boba Fett in Attack of the Clones that George Lucas created. Also, allegedly George Lucas was planning on creating a Darth Plagueis TV show. Which most likely would have changed alot, if not everything, from the James Luceno Darth Plagueis novel. So all I’m saying is the Plagueis novel is not gospel and there could be other avenues and deviation. It is however a great book, and a good source of information to get any sort of information on Plagueis and Palpatine’s rise, as of right now. If you want to check out this novel for yourself, you can here.
Additionally, in the original rough draft of Revenge of the Sith, George Lucas had a scene where he told Anakin outright that he was his father and created him. This was ultimately cut from the final draft, as George Lucas felt it was too on the nose. furthermore, Palpatine telling Anakin that Plagueis taught his apprentice everything he knew, and this would include the secrets of midichlorian manipulation. It also pairs well thematically for Palpatine to be the one who created Anakin, in regards to the chosen one prophecy. As Palpatine always talks about destiny, and later Vader would speak about destiny as well. This repetition of talking about destiny from Palpatine, illustrates that there is a mode of thought of an unchangeable future, a path set before you that you can not break from, Anakin’s destiny was to fall, and to be a servant to Palpatine, because Palpatine deemed it so by Anakin’s very creation. Anakin was created to appear to look like he was the Jedi’s prophesied chosen one, all the while being a creation of the Sith to later be used as a tool for the Jedi’s own demise, using their own beliefs and prophecy against them. Which is a very Sith way of operating. Vader’s very name is a derivative of invader. He invaded the Jedi order only to destroy it. This also goes around full circle, as Anakin/Vader breaks away from his “destiny” that Sidious laid out for him, and actually does fulfill the prophecy of the chosen one and brings balance to the force, despite being a creation of the Sith for their gain. Thematically this makes more sense.
It also works on a broader story telling level. Sidious’ plan was always to get Anakin as his apprentice. Maul and Tyrannus, were just a means to an end. Anakin was always the goal, the creation of the most powerful force being ever to exist, that would then be used as a tool for Sidious’ machinations. We see in The Phantom Menace that Naboo was the planet that the Trade Federation blockades. Naboo’s significance being a mid rim system, and homeworld of Palpatine himself, was also in proximity of Tatooine. I believe Palpatine orchestrated everything, the entire plot of the prequel trilogy. We know he orchestrated the false war of the Clone Wars. And I believe he had the Trade Federation blockade Naboo specifically, so the Jedi would get involved and then land on Tatooine when the royal ship was damaged in their escape. Planning for all that to happen. And once on Tatooine, the Jedi would find Anakin and believe him to be their chosen one. I believe Palpatine picked Tatooine specifically, an outer rim world, so the Jedi would not detect any force users that far out in the galaxy, even one as strong as Anakin, residing there. Anakin was purposefully placed in a life of slavery to harbor pain and distress, a cornerstone requirement in a Sith’s journey. And with Anakin being hidden away in the outer rim, away from the republic and the Jedi, he could go undetected, until the time was right for him to be discovered, when Palpatine decided. Then have him be inducted into the Jedi order as their chosen one, unbeknownst to the Jedi or even Anakin. That he would be the one to destroy them, having infiltrated and invaded their order, whilst planting seeds of doubt in Anakin’s head as he grew.
All this makes more sense for Palpatine to be the one who created Anakin, as it has purpose and leads Palpatine behind every single step. Vs the alternative of him being just a causality response of the force itself to Plagueis’ experimentations. But these are just my thoughts on the matter, and open to any differing opinions.