Paladins, Barbarians, and what-not aren't "fighter subtypes". They're entirely separate classes. So if it lists lvl 4 fighter as a prereq, then you must have at least 4 levels in the Fighter class to qualify for it unless you have some means of bypassing the prereqs of the feat. There are other feats (particularly the Style feats) that require either a particular level of Monk or a particular BaB (usually higher than what a monk of the required level would have). Only the particular class would qualify to meet that prerequisite; not, say, the Fighter archetype Unarmed Fighter. Now there are Archetypes for just about all classes; they modify the base abilities of the class, but are all included under the same class heading. So Fighter Archetypes such as Two-Weapon Fighter, Tactician, Unarmed Fighter, Dragoon, etc. all still qualify to satisfy Fighter level prereqs. There are also some abilities that allow you count non-fighter levels towards meeting fighter level prereqs, but these are explicitly spelled out (such as the Magus ability). Having levels in Barbarian would not qualify you for prereqs requiring a particular level of Fighter, however.
