There is no Biblical basis for Peter having a Throne on Earth. The only earthly throne mentioned in Scripture is the Throne of David, which at the present time appears to be sitting vacant. In light of God's covenant with the Jews, why do you think that the Throne of David is vacant right now?
The Catholics disagree, and would point to Matthew 16:18 and John 21:15-17, among others, as the scriptural basis for Peter's authority. And other passages which they say demonstrate apostolic succession.
Do you believe that there is a central Christian authority? Someone with unquestioned authority to determine whether or not a belief is Christian? And by "someone" I mean a person or persons, not a text. As we see, texts are subject to varying interpretations. Is there anyone who can authoritatively interpret the text?
In light of God's covenant with the Jews, why do you think that the Throne of David is vacant right now?
It is because of the covenant that the throne is vacant. And it is because of the covenant that the throne will not forever be vacant.