In what age did the race of men enter Middle-earth And J.R.R Tolkien write any books that took place in this age?

The race of Men entered Middle-earth in the First Age, specifically during the Years of the Trees. This was a period of time before the creation of the Sun and Moon, and before the beginning of the recorded history of Middle-earth as documented in Tolkien's books.

J.R.R. Tolkien did not write any books that solely focus on the First Age. However, the events of the First Age are extensively detailed in his "The Silmarillion", which covers the creation of the world, the rise and fall of the Elves, and the First Age wars against Morgoth, the first Dark Lord.

While the First Age is not the central focus of "The Silmarillion", it does provide a glimpse into the arrival of Men in Middle-earth and their early interactions with the Elves.

The First Age is a pivotal point in Middle-earth's history, laying the groundwork for the events that unfold in later ages, including the Second Age, where the rings of power are forged, and the Third Age, where the events of "The Hobbit" and "The Lord of the Rings" take place.