Hi! ok, sorry, i missunderstood i think, but would you please add more info to the question then? Because, the question implies that when your Character (Area2D) steps on a field (also Area2D) you want to trigger an effect. Then, either your character or the filed should be able to detect the other and trigger the effect. What is your other object for? what kind of node? should that other object trigger the effect? It would be useful also if you provide your hierarchy.
Anyways, what would be the problem to connect the
area_entered signal of the player, to the script of that other object, and doing what i told? it really doesn't matter where the script is, as long as its on the same tree.
And the snipeet you wrote wont work, because your field area is not child of $player, so you cannot retrieve it like that.
For me the solution is, connect the signal
area_entered to a function in the script where you trigger the effects, and then check the group in that funciton.
If you dont want to connect signal and function, then you should retrieve the area that is overlaping with player with the function
$player.get_overlaping_areas() (keep the 0 index if you only care for one), and then check the group to the area retrieved that way.