Although there are several parallel phrases in Barnabas and 1 Peter (Barn. 5.6 and 1 Pet 1:20), it is only with Polycarp that clear use of 1 Peter is found (e.g., Pol. Phil. 1.3 and 1 Pet 1:8; Pol. Phil. 10:2 and 1 Pet 2:12). The author of 2 Pet 3:1 (ca. 100-125, or possibly as late as 180) refers to the existence of an earlier letter by the Apostle Peter. Eusebius claimed that Papias (ca. 100-150) knew and used 1 Peter (Hist. eccl. 3.39.17), and he includes it in the list of the recognised books (3.25.2 and 3.3.1). Irenaeus was the first to use 1 Peter by name (Haer. 4.9.2; 4.16.5; 5.7.2), and thereafter many references are made to the book by the early church fathers. Early witnesses validate the use of the book in the church, and it does not appear to have been seriously questioned in the fourth century, even though it is missing in the Muratorian Fragment.
Lee Martin MacDonald, The Biblical Canon: Its Origins, Transmission, and Authority (Grand Rapids: Baker Academic, 2007), 395-396.