The near-sacrifice is the episode all three traditions dwell on, and they do not agree on who was nearly killed.
Genesis 22 names Isaac, and does so explicitly and repeatedly. In Jewish tradition the episode is the Akedah, the binding, and it is read at Rosh Hashanah; rabbinic commentary is preoccupied with the silences in the text, Abraham's, Isaac's, and the fact that Sarah dies at the start of the next chapter. The story is not read as a simple test passed but as something the tradition keeps returning to with unease.
The Quran narrates the sacrifice at 37:99-113 without naming the son. The identification with Ishmael became the dominant Muslim position but was not unanimous in early Islam: classical exegetes including al-Tabari record both identifications and weigh them, and some early authorities held for Isaac. The Ishmael reading became standard later. Eid al-Adha commemorates the event, and the Hajj rites are understood as retracing Abraham's, Hagar's and Ishmael's steps at Mecca.
The Christian reading takes Isaac as a type of Christ, a beloved son carrying the wood of his own sacrifice up a hill, and Paul makes Abraham the model of justification by faith rather than by law, because he was reckoned righteous before circumcision was instituted. That argument is doing work in Paul's own dispute about Gentile converts.
Three traditions therefore hold him as founder while disagreeing about which son carried the promise, which is the disagreement the shared ancestry produces rather than resolves.