The correct phrase is "admits of" because it is the right expression to use when something is allowed or tolerated. The phrase "admits under no excuse" is grammatically incorrect in English. The proper construction should be "admits of no excuse", which means there is no room for an excuse in this matter.
Here is the detailed explanation:
- Admit of: This means to allow or tolerate something, commonly used with things that can be argued, explained, or justified.
- The other options "admits over," "admits with," and "admits in" do not correctly convey the intended meaning.