Doukutsuou kara Hajimeru Rakuen Life: Bannou no Saikutsu Skill de Saikyou ni!?

In a world where crests decide one's fate, Prince Heale is born with Cave King—a crest just as worthless as he is. Deemed a disgrace to his family, he's exiled to a barren, deserted island with not a plant nor soul in sight. Alone, miserable, but determined to survive, he reaches for a pickaxe to expand the cave he intends to make his new home—and discovers the true power of his crest! It turns out Cave King makes cavern mining as easy as breathing. And as Heale digs deeper into the island, he discovers one otherworldly mineral after another. Who's worthless now? But valuable ore isn't the only thing Heale finds on his mining adventures. He soon befriends slimes and saves goblins that wash ashore. And together as one big family, they'll work to overcome any challenge on the road to developing the island into their own little paradise.

(Source: J-Novel Club)