Identity and the confusion around his name
James "son of Alphaeus" is one of the more genuinely obscure figures among the Twelve — he appears in all four apostolic lists (Matthew 10:3, Mark 3:18, Luke 6:15, Acts 1:13) but never once in a narrative scene of his own anywhere in the Gospels. Tradition often, though not certainly, identifies him with "James the Less" (or "James the younger") mentioned in Mark 15:40 as the son of a woman named Mary who watched the crucifixion, distinguishing him by size or age from James the son of Zebedee ("James the Greater"). Some traditions go further and identify him with "James, the Lord's brother" mentioned in Galatians 1:19 and prominent as the leader of the Jerusalem church in Acts 15 — an identification the Catholic and Orthodox traditions have historically favored (reading "brother" as a wider kinship term, since Mary's perpetual virginity was already an assumed doctrine by the time this tradition solidified), while most Protestant scholarship treats James the Lord's brother, James son of Alphaeus, and James the Less as probably three separate people, or at most two, rather than confidently collapsing all three into one.
This tangle is worth naming honestly rather than smoothing over: the New Testament simply doesn't give enough information to settle it, and different Christian traditions have made different identifications for reasons that are partly theological (the perpetual virginity of Mary) rather than purely historical.
Tradition of ministry and martyrdom
Later Christian tradition, with limited early attestation, holds that James preached in Egypt or Syria and was eventually martyred — accounts vary between crucifixion and being stoned or clubbed to death, with some traditions (following the Alexandrian and Byzantine calendars) claiming he was killed with a fuller's club after being thrown from a height, echoing the traditional death of James the Just (the Jerusalem leader), which is itself part of why the two figures get conflated.
Why it matters
James son of Alphaeus is a useful reminder that "apostle" in the New Testament sense doesn't mean "someone with a substantial personal story we can tell." Several of the Twelve are essentially names on a list, present at Pentecost and then vanishing from the record — ordinary men whose faithfulness mattered without producing a memorable biography. That's not a gap to be anxious about; it's a fair picture of what discipleship usually looks like for most people who take it seriously.