Lawyerskeptic said
My question was not clear. Is there any source that specifically says Peter asked to be crucified upside down because he felt unworthy?

That may be a much later tradition. Paul and possibly Peter disappeared in Rome during Nero’s persecutions together with most  witnesses, so almost all later early Christian writings about it is guesswork and legendary expansions. Even the passage in gJohn  is not specifically saying that Peter should die by crucifixion. Neither is 1 Clement any more specific.

Lawyerskeptic said
In a reader’s mailbag, Bart said:

 The first actual description of Peter’s death in Rome is in a legendary account known as the Acts of Peter from the second century.  This is the famous account of Peter being crucified upside down during the persecution of the emperor Nero in 64 CE.  (It is widely thought – completely incorrectly – that he wanted to be crucified upside down because he did not think he deserved to die in the same way as Jesus; in fact, this story indicates that he did so in order to teach a lesson to those watching, that we see everything upside down and backwards from the way God wants us to see things).

 Does anyone have any idea where this idea came from the Peter consider himself unworthy? I can’t find any source up to and including Eusebius. There is a pretty big gap between Eusebius and modern times. I cannot nail it down. I ask because I think it is a curious example of how things get exaggerated. The Acts of Peter explained why Peter was hung upside down, but a simpler and more inspiring reason was needed.

The earliest church father to mention it is actually Origen.  In The Acts of Peter we get a speech from Peter in which he says: “But it is time for you, Peter, to surrender your body to those who are taking it. Take it, then, you whose duty it is. I request you therefore, executioners, to crucify me head-downwards in this way and no other.”  As far as written proof of any of this that’s all we have.  The added bit that Peter requested to be buried upside down has either not been passed down to us, or was an oral tradition or was simply a later re-interpretation of what The Acts of Peter actually said.