It’s a boy! HRH Master Archie Harrison Mountbatten-Windsor, the newborn son of Prince Harry Duke of Sussex and US-citizen HRH Lady Meghan Markle Duchess of Sussex, was born in the early morning of 6 May 2019. (No, Master Archie is not (yet) a Prince; that style must be conferred on him by The Queen.)
In case anyone was wondering, the young Prince is a dual US-UK citizen. He has UK citizenship from his UK father. By §301 of the Immigration and Nationality Act, US citizenship is transmitted to him automatically because he is the child, born in wedlock, between a US citizen (Lady Meghan) and a foreigner (Prince Harry). The Lady Meghan may or may not be a UK citizen at this time, but that does not matter. For purposes of transmission of citizenship, at the time of Master Archie’s birth, all that counts is that she is a native-born US citizenship who has lived most of her life in the USA.
Master Archie will have a US passport — issued by the US Embassy in London. He will not need a green card or a visa to enter the USA.