Darth Sidious fears Luke Skywalker in the same way he feared Anakin before he managed to manipulate him into becoming his apprentice. He fears how powerful he can become. When Yoda fought Darth Sidious and then escaped, why couldn't Palpatine sense his presence?
DARK SIDE FRIDAY - Did you know Palpatine feared Qui-Gon Jinn? Palpatine was immensely powerful and he could see the future which made him very confident about pretty much anyone who stood against him. So why Qui-Gon Jinn?
Brand reveals that Palpatine isn't entirely composed of hate, but also of fear, and in comforting the dying Brand, Luke Skywalker explains, "More than anything, the Emperor fears obliteration in the dark side." For all his posturing, Palpatine still fears death and the consequences of his use of the dark side.
Dying is the only ongoing fear that Palpatine had. There is one time, that I know of, in Legends where it is said that Palpatine is afraid of someone, and that someone is… (drumroll)… Luke.
Because Dooku was very powerful, far more powerful than Sidious thought he was when he recruited Dooku, and if Dooku attacked him with someone like Ventress by his side, he could pose a serious threat to him.
Another contender for the weakest Sith could be Count Dooku, or has he's also known Darth Tyranus. Dooku was a cunning and talented Sith Lord, known for his swift skills with a lightsaber and his ability to manipulate populations.
Bottom line, Dooku never considered himself a Sith. And he wasn't; he was a man looking to change the galaxy in a way the Jedi were unwilling to try. And that is why he joined the Sith and became Darth Sidious' apprentice, Darth Tyrannus. When Dooku became Sidious's apprentice, he was already an elderly man.
Wilhuff Tarkin
Like Vader, Tarkin was one of Palpatine's most trusted followers.
Emperor Palpatine admitted to fearing Luke Skywalker and even said that if he had him by his side instead of Kylo Ren, he would have won the galaxy.
Palpatine absolutely did NOT fear Kenobi as a physical threat to himself. Could he have beaten Obi-Wan in a straight lightsaber duel? Possibly. Let's compare their forms.
As powerful as Darth Sidious may have been, it's easy to forget he actually seemed afraid of Master Yoda. As seen in Revenge of the Sith, Palpatine initially thought he could deal with the aged Jedi Master - and then, when Yoda proved able to counter the Sith Lord's Force lightning, he fled.
Even after his brutal scorching in the fires of Mustafar, sand remained the only natural phenomenon that Vader feared. To him, sand was a reminder that he'd failed to save his mother or Padme from death.
Jedi Masters Mace Windu, Kit Fisto, Saesee Tiin, and Agen Kolar confronted Chancellor Palpatine upon learning of his secret identity as a Sith Lord.
A Sith Lord with the ability to prevent death and create life, Plagueis is the mentor of Sheev Palpatine/Darth Sidious, who, in accordance to the Sith's Rule of Two, eventually betrays Plagueis by murdering him in his sleep, taking his place as Sith Master.
Amedda was one of the few beings in the galaxy who knew Palpatine's secrets, most notably his true identity as a Sith Lord.
Thus, while Qui-Gon was less powerful than Yoda, Palpatine feared him more.
He was still completely unaware of the Sidious/ Palpatine connection until ROTS. He also said during TCW season 6 that the Jedi order must believe in the clones and end the war before the Sith's plans are realized.
First on the list of Palpatine's rivals is Darth Bane. He was not only unrivaled with a lightsaber in his day, but he was also a master at shrugging off the force powers of others, Sith and Jedi alike. As the sole surviving Sith of the Jedi-Sith War, his knowledge of the force should not be underestimated.
Tarkin was the embodiment of Palpatine's desire to rule by fear and was put in charge of the Death Star project. In many ways, Tarkin was more ruthless than Palpatine.
Sate Pestage was Palpatine's long-time ally and confidant.
His former colleagues in the Jedi Order saw Dooku as misguided but a man of principles, and refused to believe he could be an advocate of violence and war. They were wrong; Dooku had sworn allegiance to the Sith Lord Darth Sidious, taking the name Darth Tyranus.
Revenge of the Sith (2005)
Anakin gives in to his hatred of Dooku and uses his anger to overpower him, severing both of Dooku's hands and leaving him helpless.
Qui-Gon Jinn was called a Grey Jedi by his peers for defying the council in training Anakin Skywalker (and then passing his training on to Obi-Wan Kenobi).