Did the Shah of Iran have any illegitmate children?

I wouldn't rule it out, maybe as an "experiment" to determine if the
lack of offspring in his first marriage was a male fertility problem.

But if he did, and we haven't heard about it yet  - and the rainbow
press has made much wilder claims about other celebrities -  I don't
expect that we ever will.

If he did, you can be sure that they would have been hushed up.

The Shah of Iran did not have any illegitimate children. There has
been no creditable document indicating this issue. The only document
that has some indication about Shah of Iran having illegtimate child
was made by the Islamic government of Iran after the Islamic
revolution of 1979. The islamic government looks at Shah and his
family as a treat, therefore after the revolution the Islamic
government started to spread many lies about the way the King of Iran
(Shah) was living. however, no accredited historian has ever
documented any thing about illegitimate child.

>> The islamic government looks at Shah and his family as a treat...

I doubt this. A threat, maybe. Certainly not a treat.

'A treat' in the sense that his head would have been served as the main course.