Dry and white patch can be due to many diseases in skin like allergy, infection, etc.
Proper examination of that patch and also other areas is necessary for correct diagnosis and treatment.
If needed we have to do a biopsy of skin where we take a part of skin and send to the lab for checking particular infection.
Next Steps
Consult a qualified dermatologist and get it examined thoroughly
Health Tips
Don't use self medications or steroid cream like mometasone unless it is prescribed by a qualified dermatologist after making proper diagnosis.Hope this helps.