Does morphea cause cancer?

No: The premalignant potential of the common, patchy, linoleum-like skin lesion is near-zero. Reports i've heard of cancers arising near these sites sound like coincidences, or people just watching them closer.

It does not. Morphea is a benign skin disorder. It is localized scleroderma, "hard skin," that usually involves the chest, abdomen, or limbs. It is uncommon to be on the hands or face. It can be treated, but not always resolved. Please see a dermatologist.