Short answer
– The Gospel of John (which contains John 6:35) is most likely written by John the Apostle — the son of Zebedee and one of Jesus’ inner circle — according to the traditional evangelical position.

Who John was (evangelical summary)
– One of the Twelve, brother of James, a fisherman called by Jesus (Mark 1:19–20).
– Part of Jesus’ inner three (Peter, James, John) present at key events: Transfiguration, raising of Jairus’s daughter, Gethsemane.
– Referred to in John’s Gospel as “the disciple whom Jesus loved” (e.g., John 21:20–24). Evangelicals typically identify that beloved disciple with the apostle John.
– Later tradition (accepted by many evangelicals) places him ministering in Ephesus and possibly exiled to Patmos (Revelation).

Why many evangelicals accept John the Apostle as the author
– Internal witness: the Gospel, while anonymous in Greek, repeatedly points to an eyewitness tradition and identifies the “disciple whom Jesus loved” as an authoritative witness (John 21:24). Evangelicals argue the level of intimate detail (private conversations, interior movements, specific locations) reflects an eyewitness source.
– Early church testimony: early Christian writers (Papias as reported by Eusebius, Irenaeus, Clement of Alexandria, Tertullian) attribute the Gospel to John the Apostle. Evangelicals treat this early testimony as significant evidence.
– Theological and linguistic unity: the Gospel’s distinctive theology (high Christology, “I am” sayings, emphasis on belief leading to eternal life) and its connection with the Johannine epistles and Revelation are taken as consistent with apostolic authorship.
– Scholarly defense: many conservative and evangelical scholars (e.g., D. A. Carson, Leon Morris, Andreas J. Kostenberger) argue for Johannine apostolic authorship and an authorship context centered in Ephesus or the surrounding region late in the first century.

Date and place (common evangelical view)
– Likely written in the late first century, often dated c. 85–95 AD.
– Probable locale: Ephesus or nearby Asia Minor, where Johannine Christianity had a strong presence.

How this affects reading John 6:35
– If John the Apostle wrote the Gospel, John 6:35 (Jesus’ “I am the bread of life” statement) carries the force of an eyewitness testimony about Jesus’ self-claims and their meaning. Evangelicals therefore read the verse as both historically grounded and theologically authoritative: Jesus is the true sustainer of spiritual life and the object of saving faith.

Recommended evangelical resources for further study
– D. A. Carson, The Gospel According to John (Pillar Commentary)
– Leon Morris, The Gospel According to John (NICNT)
– Andreas J. Kostenberger, John (BECNT)
– For patristic testimony: Irenaeus, Against Heresies (on John’s authorship)

Note
– Some critical scholars propose alternative authorship theories (a Johannine community, “John the Elder,” composite authorship, etc.). Evangelicals generally consider these less convincing and favor the apostolic authorship on the grounds above.