The letters (epistles) of First and Second Peter were written by Peter (Cephas,
Simon, son of Jona, native of
Bethsaida, lived with his wife in Capernaum)
who was one of Jesus' learning-disciples (refer to Matthew 4:18 and Acts
1:13).
Peter was the apostle who was there when the resurrected Lord Jesus
Christ made it available for people of the Judean / Israeli background
and of the Gentile / other-nation background to become holy-people
(Christians) by receiving the gift of holy spirit (refer to Acts
chapters 2 and 10). Peter wrote to holy-people (Christians) feeding the
flock with God's Word.
The letter of I Peter was written between 60 - 64 AD
from Babylon; II Peter was written between 61 - 65 AD.