Most of the story around this dispute comes from the Jews and Christians (Isra'iliyat narrations), but have questionable validity hence they will not be mentioned here. Allah knows best.

David was known as a man of justice amongst his people. He advised his people on an issue described in Surah Sad. He had a son named Solomon (Sulaiman), who was intelligent and wise from childhood. When the following story took place, Solomon was eleven years old.

One day, David was sitting, as usual, solving the problems of his people when two men, one of whom had a field, came to him. The owner of the field said: "O dear Prophet! This man's sheep came to my field at night and ate up the grapes and I have come to ask for compensation." David asked the owner of the sheep: "Is this true?" He said: 'Yes, sir." David said: "I have decided that you give him your sheep in exchange for the field." Solomon, to whom Allah had given wisdom in addition to what he had inherited from his father, spoke up: "I have another opinion. The owner of the sheep should take the field to cultivate until the grapes grow, while the other man should take the sheep and make use of their wool and milk until his field is repaired. If the grapes grow, and the field returns to its former state, then the field owner should take his field and give back the sheep to their owner."

David responded: "This is a sound judgement. Praise be to Allah for gifting you with wisdom. You are truly Solomon the Wise."

Has the story of the two plaintiffs, who scaled the ˹wall of David’s˺ sanctuary, reached you ˹O Prophet˺?38:21

When they came into David’s presence, he was startled by them. They said, “Have no fear. ˹We are merely˺ two in a dispute: one of us has wronged the other. So judge between us with truth—do not go beyond ˹it˺—and guide us to the right way.38:22

This is my brother. He has ninety-nine sheep while I have ˹only˺ one. ˹Still˺ he asked me to give it up to him, overwhelming me with ˹his˺ argument.”38:23

David ˹eventually˺ ruled, “He has definitely wronged you in demanding ˹to add˺ your sheep to his. And certainly many partners wrong each other, except those who believe and do good—but how few are they!” Then David realized that We had tested him so he asked for his Lord’s forgiveness, fell down in prostration, and turned ˹to Him in repentance˺.38:24

So We forgave that for him. And he will indeed have ˹a status of˺ closeness to Us and an honourable destination!38:25

Tafsir on these verse by As-Sadi explains: Having told us that He gave His Prophet Dawood sound judgement when judging disputes among people, for which he was well known, and people would seek him out for that reason, Allah now tells us the story of two disputants who came to him concerning an issue that Allah made a test for David and a lesson, because of a mistake that he made. But Allah had mercy on him and forgave him.

​​With regard to the mistake that David made (and for which he sought forgiveness), Allah does not tell us what it was, because there is no need to do so. Therefore trying to find out what it was is unnecessary. Rather what matters in the story that Allah tells us here is His kindness towards him, and that he repented and turned to Him and was raised in status thereby, so that after repenting he was better than he was before.