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I have reviewed the attached photographs (attachment removed to protect patient identity).
This condition is not due to any vitamin deficiency or any other deficiency. This is keratolysis exfoliativa which is a form of eczema. It does not cause any irritation or itching.
You just need to apply moisturizing cream containing White Soft Paraffin frequently and liberally on hands and feet.
Along with this avoid frequent washing of hands and feet; avoid hard soaps and use gloves while cutting and washing activities. This will definitely help you.
For further information consult a dermatologist online --> https://www.icliniq.com/ask-a-doctor-online/dermatologist