Paladin default magical power source in 5e is their vow, not believing in themself.
PH page 82:
"Whether sworn before a god's altar and the witness of a priest, in a sacred glade before nature spirits and fey beings, or in a moment of desperation and grief with the dead as the only witness, a paladin's oath is a powerful bond. It is a source of power that turns a devout warrior into a blessed champion."
"A paladin swears to uphold justice and righteousness, to stand with the good things of the world against the encroaching darkness, and to hunt the forces of evil wherever they lurk. Different paladins focus on various aspects of the cause of righteousness, but all are bound by the oaths that grant them power to do their sacred work. Although many paladins are devoted to gods of good, a paladin's power comes as much from a commitment to justice itself as it does from a god."
5e is a little unclear and contradictory on the role of gods here.