Likely related to Yasmin or Asma, giving it associations with jasmine or elevated rank.
Yasma is almost certainly a variant or diminutive of Yasmin — from the Persian "yasaman," the jasmine flower, which traveled through Arabic as "yasmin" and spread across the Islamic world and eventually into European languages during the medieval period of cultural exchange through Andalusia and the Crusader states. Jasmine itself became one of the defining fragrances of the medieval Arabic poetic tradition, appearing in the ghazals of Hafez and Rumi as an emblem of beloved beauty, transience, and sweetness. The flower's white blossoms opening at night gave it an association with mystery and the feminine.
The clipped form Yasma likely emerged in Central Asian, Turkish, or North African naming traditions, where shortened and softened variants of classical Arabic names are common practice — much as Fatma derives from Fatima, or Zeinab contracts from Zaynab. The name carries the jasmine's floral delicacy while shedding the more familiar suffix, giving it a quality of intimate abbreviation, the name a family uses at home. In parts of the Levant and Maghreb, such forms are considered more affectionate than formal.
For contemporary parents, Yasma threads an appealing needle: it sounds immediately beautiful to ears across cultures, carries a rich Persianate and Arabic heritage, and yet remains unusual enough that most English-speaking listeners encounter it as something genuinely new. The jasmine association — purity, warmth, the perfume of Mediterranean evenings — gives it an effortless sensory quality that many parents find irresistible.