Here are a couple of examples from the Renaissance and not the middle ages.
Edward VI 1537-1553) became king of England in 1547 age nine under a regency. Henry VIII's will established a council of regents until Edward VI reached the age of 18.
Since Edward died aged 15 years, 8 months, and 24 days, he never achieved his legal majority and the regency council had the legal right to make decisions for him during his entire reign.
Edward VI was intelligent and well educated, and historians have speculated how much the regency council considered his opinions and whether Edward would reverse their decisions when he came of age.
As Edward was growing up, he was able to understand more and more government business. However, his actual involvement in decisions has long been a matter of debate, and during the 20th century, historians have presented the whole gamut of possibilities, "balanc[ing] an articulate puppet against a mature, precocious, and essentially adult king", in the words of Stephen Alford. A special "Counsel for the Estate" was created when Edward was fourteen. Edward chose the members himself. In the weekly meetings with this Council, Edward was "to hear the debating of things of most importance". A major point of contact with the king was the Privy Chamber, and there Edward worked closely with William Cecil and William Petre, the Principal Secretaries. The king's greatest influence was in matters of religion, where the Council followed the strongly Protestant policy that Edward favoured.
I once read a biography of Edward VI that stated that when Edward wanted to forbid his half sister Mary to have catholic worship, Mary's cousin Emperor Charles V threatened to invade England with a Spanish and Dutch armada and conquer it unless Edward agreed to let Mary worship as she wished. The biography said that it took the council members hours of arguing and pleading with Edward that they had to save England from conquest by letting Mary have Catholic worship before Edward agreed to it.
I also read somewhere that at one Christmas celebration Edward stated that the ceremonies seemed superstitious, and that the reforming group took that as grounds to proceed swiftly with making the Church of England more Protestant. And the writer of that account claims that shows that Edward VI was actually the most absolute monarch in English history, even more so than his father Henry VIII.
When Edward VI was dying in 1553, the government decreed that his half sisters Mary and Elizabeth were not eligible to inherit the throne, and that the throne should go to their cousin Lady Jane Gray.
For centuries, the attempt to alter the succession was mostly seen as a one-man-plot by the Duke of Northumberland. Since the 1970s, however, many historians have attributed the inception of the "devise" and the insistence on its implementation to the king's initiative. Diarmaid MacCulloch has made out Edward's "teenage dreams of founding an evangelical realm of Christ", while David Starkey has stated that "Edward had a couple of co-operators, but the driving will was his". Among other members of the Privy Chamber, Northumberland's intimate Sir John Gates has been suspected of suggesting to Edward to change his devise so that Lady Jane Grey herself—not just any sons of hers—could inherit the Crown. Whatever the degree of his contribution, Edward was convinced that his word was law and fully endorsed disinheriting his half-sisters: "barring Mary from the succession was a cause in which the young King believed."
So even though Edward VI never reached his legal age of majority, I can remember three accounts of Edward's will and actions allegedly changing the course of English history. If those accounts are correct the regency council apparently feared punishment after Edward reached his majority and took power if they took actions that he strongly opposed.
King Francis II of France (19 January 1544-5 December 1560) lived to be 16 years, 10 months, and 16 days old. He became King of France on 10 July 1559 aged 15 years, 5 months, and 16 days old.
According to French law, Francis at the age of fifteen was an adult who in theory did not need a regent. But since he was young, inexperienced, and in fragile health, he delegated his power to his wife's uncles from the noble House of Guise: Francis, Duke of Guise, and Charles, Cardinal of Lorraine. His mother, Catherine de' Medici, agreed to this delegation. On the first day of his reign, Francis II instructed his four ministers to take orders from his mother, but since she was still in mourning for the loss of her husband, she directed them to the House of Guise.
As far as I know, Francis II probably simply rubber stamped the decisions made by his mother Catherine and the Guises. If Francis did personally decree anything, it probably would have been instigated by his strong willed wife, Mary Queen of Scots.
So the differences between the reigns of Edward VI and Francis II are in large part due to how different their personalities were.
And in the Renaissance society and government was similar to in the later Middle Ages, so there should have been similar variations during the Middle Ages.