No, King Charles III did not try to marry his cousin. While marrying a cousin was common in royal families historically, it is not a practice that is currently encouraged or considered acceptable. King Charles is married to Camilla, Duchess of Cornwall, who is not his cousin.
King Charles's father, Prince Philip, was a distant cousin of Queen Elizabeth II. They were both descendants of Queen Victoria. However, this relationship was not considered close enough to be a concern for their marriage.
It's important to note that the practice of marrying cousins has declined significantly over time due to increased awareness of the potential genetic risks associated with such unions.