Lord: Treasure Hunting on the Map

[Western fantasy, nobility, territory development, a minor golden finger, inventing, building a powerful army, no useless protagonist]

He transmigrates to another world as the third son of a count and is granted a remote little town. With the golden finger known as the [All-Knowing Map], he can keep everything under control: mountains and rivers, mineral deposits and hidden treasures, even enemy troop movements! Developing land, raising troops, waging wars: from barren lands to an iron-blooded empire, I will map out my own domain!

The golden finger doesn't play a major role. Its detection range is too small to be of much use, and at first it's mainly a way for the protagonist to find treasures and secure start-up funds.

Once he reaches his territory, he won't immediately start prospecting for minerals. After all, even if he finds a deposit, he won't be able to hold on to it without the strength to defend it. Later, when the map's detection range expands, it becomes much more useful.