I've never heard that he had an illegitimate daughter.
Why? Probably simply because the laws in Spain are different than the laws in any other country (any country has their own laws).
Also, likely, on the precedent that Juana la Beltraneja, the chief competitor to Ísabel la Católica, was the daughter of the queen, of that, there was no doubt, but most people assumed her father was a lover of the queen's, making her illegitimate...the lover's name: "Beltrán", hence the moniker.
Her supporters knew the rumors, and assumed them to be untrue, but also supported her despite being (allegedly) illegitimate. She would have been queen, anyway, had her army won the civil war.
Betcha didn't know that tidbit of Spanish history, did you? :) (read up on it...it's on the web).
BTW, she couldn't be fourth in line, because his legitimate children come before her.
The line of succession is:
Felipe
His daughters
Elena
Her children
Cristina
her children
THEN, if she's truly in line for the throne, Paola de Robilant
You know, what? I'm going to look up the veracity of that.
This site doesn't mention any such person: http://en.wikipedia.org/wiki/Line_of_succession_to_the_Spanish_throne
From what I can find, quickly, there is no proof that he is her father, and the mother was a bit of a playaround (to put it kindly) and Paola DI Robilant could be the daughter of pretty much anyone.
I don't see her listed as any sort of official pretender to the throne, nor are the accounts even supportable, since the book where the claim originates was written under a pseudonym, by an unknown author...no one to substantiate said claim.
*edit* Apparently, ZAVALA thinks so...and that's clearly not the stand of anyone official. HE may put her there, but it doesn't look like she IS. It also doesn't look like the king has ever acknowledged her in any way.
*2nd edit* Just because someone wrote a book, and published it, and it has caused a furor, does NOT make it so, nor does the fact that this author claims this illegitimate person is fourth in line for the throne make it so. Clearly, he was stating what HE thought should be, NOT the facts.
If the King has not acknowledged an illegitimate child, then that child can't make any claims to ANYTHING! And it doesn't sound as if she has tried.