What are the sources that claim that she was the daughter of Adolf Fredrik? I have read this before, but I haven't any good sources for this information.
Eleonora Charlotta was born March 31st 1799 in Stockholm, baptized in Sankt Katarina, Stockholm, April 2nd. The persons mentioned as her parents are Carl Magnus Löfstedt and Ulrica Brunström.
Carl Magnus Löfstedt and Elisabeth Ulrica Brunström was married in Sankt Katarina Nov 18th 1798, she is allready preagnant at that time!
Ullrica Elisabeth Brunström was born in Hudiksvall June 29th 1776, baptized June 30th, of parents Jonas Brunström and Elisabeth Malmgren.
So who is the biological father of Eleonora Charlotta?
Fredrik Adolf had a daughter with his official lover Sophie Hagman. Nothing was done to cover that up. From 1797 to 1800 he had a relationship with actress Euphrosyne Löf.
At this point of time it was not the normal thing that children produced out of wedlock by royalty would be just covered up and unknown and unheard of, just to magically turn up in genealogical data from descendants of the alleged children some hundred years later.
Verifying sources from the time is the only thing that could PROVE that this Eleonora Charlotta would actually have been fathered by Fredrik Adolf.
Eleonora Charlotta is entered in an ancestral file on ancestry.org where she is called Eleonora Charlotta Carlsdatter and have her parents clearly listed as the offical ones as in the book of births from S:ta Katarina parish. Also noted is "også referert til som Eleanora Charlotte Carlsdatter Lövsted
So the claim that she called herself Fredriksdatter in the censuses of 1865 and 1875 seems very weak. They are supposed to be searchable online at the Norwegian national archive web site, but no matter what spellings I try, I don't find Eleonora there.