why are small green patches showing up on my iphone 11 screen randomly

Hello~ Try a forced restart…

Force restart iPhone - Apple Support

If no joy you may need to have your iPhone checked out…

Genius Bar Reservation and Apple Support Options - Apple

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Has your iPhone been wet or have you dropped it?

~Katana-San~

If the green "patches" continue to appear after you have performed a Forced Restart, this is very likely an indication that the screen digitizer is failing and the screen will need to be replaced.

If you have not yet replaced the battery, it is also very likely due to be replaced at this point if it is under 80% Maximum Capacity. Settings > Battery > Battery Health & Charging

Make an appointment at the Apple Store or take the phone to an authorized Apple service shop in your area to get them check out and test the phone.

Genius Bar Reservation and Apple Support Options - Apple

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Why are the green patches appearing?

This can usually happen due to internal hardware issues. Or software issues. Like the others said, try restarting or powering it off. If that fails, I recommend you get it fixed.

Can you post a screenshot of this behavior so we can see exactly what you are referring to?