This is an idiom with no settled meaning. Some people consider it an insult, others a term of endearment.
The most common usage is by the character of The Joker in the Batman universe. He describes himself as “The Clown Prince of Crime.” But did it predate that?
According to a Google NGram search, usage of the phrase “clown prince” peaked in about 1940, which is corresponds to when The Joker was introduced in the Batman comics – April 25, 1940. I couldn’t find the full content of that issue, so I don’t know if the phrase “clown prince” was actually used, but Batman fandom uses the phrase to refer to The Joker as a matter of course.
The earlier Google search did show some usage of the phrase prior to 1940, but I can’t find much in terms of specifics. Every search is dominated by references to The Joker.
In an article about comedian pianist Victor Borge:
It is this immortal combination of skill and humour which earned the man the title, “The Clown Prince Of Denmark.”
In a discussion about a Masked Singer character:
This clown prince, Season 6’s latest and weirdest wild card, was perhaps the scariest character in Masked Singer history …
The character in that article was a jester, which might have some bearing: a jester was a clown that entertained royal families. Perhaps a jester is a “clown prince”? I couldn’t find any proof of this, but the usage seems to fit.
As an idiom, what does it mean? It appears to mean a singularly celebrated comic figure. It tends to be qualified with a domain – you are the “Clown Prince of Crime” or the “Crown Prince of Denmark” or “football’s clown prince.”
It can also be used as an insult. Recently, the Indian Finance Minister said this about the head of Congress:
The world’s largest democracy must seriously introspect whether public discourse should be allowed to be polluted by the falsehood of a “Clown Prince.”
That apparently inflammatory remark got lots of press in India.