Its funny, in both the AD&D 1e and 2e PH paladin descriptions there is no mention of gods. The closest is the 1e tithing requirement "An immediate tithe (10%) of all income — be it treasure, wages, or whatever — must be given to whatever charitable religious institution (not a clerical player character) of lawful good alignment the paladin selects." and the similar 2e one "A paladin must tithe to whatever charitable, religious institution of lawful good alignment he serves. A tithe is 10% of the paladin’s income, whether coins, jewels, magical items, wages, rewards, or taxes. It must be paid immediately."
They just get clerical spells and powers and unique paladin powers and their alignment and code restrictions.
In 3e they are tied to and powered by divine power but not the gods.
3.5 PH page 43: "Religion: A paladin need not devote herself to a single deity—devotion to righteousness is enough. Those paladins who do align themselves with particular religions prefer Heironeous (god of valor) over all others, but some paladins follow Pelor (god of the sun). Paladins devoted to a god are scrupulous in observing religious duties and are welcome in every associated temple."
It is only in the 4e PH that Paladins core need a deity.
"Paladins are indomitable warriors who’ve pledged their prowess to something greater than themselves. Paladins smite enemies with divine authority, bolster the courage of nearby companions, and radiate as if a beacon of inextinguishable hope. Paladins are transfigured on the field of battle, exemplars of divine ethos in action.
To you is given the responsibility to unflinchingly stand before an enemy’s charge, smiting them with your sword while protecting your allies with your sacrifice."
"Warriors wielding divine power can be found in the service of any deity, even evil or chaotic evil ones."
"As fervent crusaders in their chosen cause, paladins must choose a deity. Paladins choose a specific faith to serve, as well as an alignment. You must choose an alignment identical to the alignment of your patron deity"