Hi, my question is, if a AOE attack that will trigger fire continous effect, when the attack is missed, the model is hit by a blast damage, but does it takes the continous fire effect?
The answer is: it depends.
In the simple cases of Continuous Effect Fire or Corrosion weapon qualities and a direct hit: yes. Every model in the AOE (barring exceptions due to other special rules) will be affected by the Continuous Effect. That is because those weapon qualities just require a model to be “hit” by the attack, and all the models are hit. This also applies to Critical Corrosion/Fire, if the attack directly hits.
Continuous Corrosion/Fire also also applies the continuous effect to the target (and only the target) in the event of a miss, because the continuous effect only requires a “hit” , and although the attack roll failed to equal or exceed the model’s DEF (or because of Stealth or whatever), the model was still hit.
However, in the case of an AOE attack with critical effects that does not directly hit: no. This is because a critical hit is required, and a critical hit requires you to directly hit. And, obviously, a miss is not a direct hit.
Hopefully that makes sense!