Capernaum's synagogue ruins sit on top of an older, different synagogue, and the gospels imply Jesus taught in whichever one stood there first.
A synagogue built over a synagogue
The visible white limestone synagogue ruins at Capernaum date to several centuries after the first century, but excavation beneath its floor revealed foundations of an earlier synagogue built from local black basalt, plausibly the synagogue described in the gospels as a site of Jesus's teaching and a recorded healing, meaning the building visitors see today is a later monument constructed directly over the more historically relevant original structure rather than being that structure itself.
The town Jesus made his base
The gospels describe Capernaum functioning as a base for Jesus's ministry after he left Nazareth, referred to in one gospel as "his own town," and record specific episodes there including the healing of a Roman centurion's servant, giving the town a distinct narrative role as an operational centre rather than merely one stop among many on an itinerant journey.
As this entry's companion article covers
The identification of a specific house, built over in the Byzantine period by an octagonal church structure, as the traditional home of the apostle Peter, is addressed directly in this entry's companion article rather than repeated here.