Yes, dodging still applies to spells cast by an Elemental Adept
Elemental Adept states that:
Spells you cast ignore resistance to damage of the chosen type.
The ranger's evasive function states:
If you are exposed to an effect, such as the fiery breath of a red dragon or a lightning spell, which allows you to make a skill-saving throw that does half the damage, you will not suffer damage if you successfully do the save throw half damage if you fail.
Evasion does not give you resistance or immunity to harm, it simply halves or reduces the damage you take to zero – which has the same numerical effect as resistance or immunity, but is actually not resistance or immunity. Since dodging does not provide resistance, Elemental Adept does not overcome it – the two functions have no interaction with each other.
Apart from that, this also means that while multiple sources of resistance to the same damage don't stack, dodge and resistance can both be applied to incoming damage, so a ranger with a relevant resistance can take damage over and over again from an enemy effect, which reduces it to only a quarter.