Shot in the dark, but are you
An unsolvable riddle
By definition I cannot exist, but paradoxically my name can be the solution
Riddles have solutions, even if they are difficult to piece together. However, an unsolvable riddle can be the solution to this riddle.
You cannot solve me, but can conclude and resolve me.
An unsolvable riddle cannot, of course, be solved. However, you can conclude that you cannot solve the riddle, and therefore resolve the riddle.
You can try to figure me out, but you cannot figure me out.
Naturally, you can try to figure out an unsolvable riddle. However, you cannot actually figure out an unsolvable riddle.
As for the clue:
"If I have you eternally riddled, that is my specific intention"
Well, if you're stumped forever, then of course the riddle has been unsolvable.