During the reign of William III & Mary II in 1692 the International Statute of Wizarding Secrecy was signed, separating the lives of the magical and the muggles. The reign of the muggle royal family over the magical population of Britain - and later the United Kindgom - was largely undisturbed; both British societies observed the same monarch until the pure-blooded of the magical society began demanding detachment. From what started as being general discontent grew into violent actions with a magical civil war approaching over the horizon. In a stroke of luck that avoided turmoil, the ruling King George III had a magical daughter hidden from the muggle society. This daughter, Princess Charlotte, was quickly installed as the monarch of the magical society of Britain - an act which finally separated the two.
The arrangement worked out perfectly for both societies; whilst both monarchies were separate, the two worked closely to ensure similar values were shared and upheld. When the muggle monarchy changed their house name to Windsor, the magical monarchy followed suit. Everything was harmonious until the ascension of King Henry II. A monarch who wanted to devolve the power of the Ministry itself, Henry became tyrannous early on in his reign. Turmoil that threatened to overthrow the monarchy rose again, saved only by the forced abdication of Henry and the replacement by his eldest daughter, Victoria.
Proving to be the saving grace of House Windsor, Queen Victoria remedied her father's mistakes. She appealed to all crowds of magical life; advocating for no discrimination for species, being proud enough of her pure-blooded heritage to satisfy those who cared whilst remaining completely relatable for all. Her reign, still going strong, has remained among the most harmonious and popular since the magical monarchy's establishment.
Princess Mary is the second-born child and eldest the daughter of Queen Victoria and Prince Louis. Out of their six children, she had always been the most passionate and interested about Muggles and their lifestyle, which was why it turned out to be no surprise when she ended up marrying a muggle-born wizard, Colin, whom she met in muggle primary school. They ended up going to Hogwarts together and embarked on a relationship with each other, marrying after 20 years since they've first met. After the wedding, Colin took on the name Cornelius, which he deemed more fitting.
They soon had their first son whom they named Archibald Alexander Louis - Archie for short. Prince Archie was the first and eldest grandson of the Queen, and thus was rather spoilt. It didn't have too much of a negative impact on him though, because he grew up to be generous and kind, especially to his younger sister, Elenore, and his royal cousins whom he's all close too. He is actually very protective of everyone, often acting like the 'big brother' of everyone in the family, and would never let anyone hurt them.
His first sign of magic occurred when he was eight years old. He was with his parents on a diplomatic visit to the magical royal family of Sweden, and he accidentally bewitched some snowballs while he was out playing with the other children. After that incident, he was deemed eligible to study at Hogwarts and received his letter of acceptance the eve of his eleventh birthday.
He went to school, got sorted into Hufflepuff house, did well, and graduated with excellent marks. He made tons of good connections with the people he encountered - students and teachers alike - and was very well-known during his time at school (being a prince, and all). After graduation, Prince Archie didn't immediately look for a job. Instead, he stayed unemployed and enjoyed the perks that come with being a free adult (of royal lineage) and is currently busy travelling the world and going on a bunch of crazy adventures. He doesn't have a career in mind yet, despite being twenty-four years old already, but he is sure that the universe will send him a sign soon, and that he'll know what he'll want out of life. For now, he's kicking back and enjoying his free time.