The Protection fighting style is described (SRD, p. 24) as:
When a creature you can see attacks a target other than you that is within 5 feet of you, you can use your reaction to impose disadvantage on the attack roll. You must be wielding a shield.
Picturing a scenario where a creature (presumably an ally) is beside you and is attacked by an enemy, the Protection fighting style is used. It raises the following questions:
- Does the reaction make the Paladin move in between the Attacker and creature you were protecting?
- Should the movement be deducted from the Paladin's available movement next turn?
- If the Paladin moves in between the two creatures, which position should it take? The attacker's (moving the attacker one tile away) or the protected creature (moving it behind the Paladin)?
No, the Protection Fighting Style does not move the Paladin
The full text you give says:
I've highlighted the only mechanical benefit you gain as a Paladin. You grant a disadvantage to their attack roll, nothing more, even if the visual is you trying to protect them with your shield.
Consider that, in grids, characters do not actually occupy the full 5ft x 5ft square they are standing on (people are not 5'x5' cubes). Instead, they just "control" that square. So you can imagine that your Paladin moves inside their space enough to try to protect their ally, without actually standing in the way of the attacker.