King Karl XIV Johan - Daughters??

[David]

Did Swedish King Karl XIV Johan (formerly Jean Baptiste Bernadotte) have any daughters, legitimate or otherwise?  You will recall this king ruled from 1818-1844.  How would I find out if so, what their names were, ages, etc.  
 
Thanks.
 
David

[Elisabeth Thorsell]

At least officially he had only one son, the future king Oscar I, born in 1799. I have heard about one illegitimate son, but no daughters.