This is the 9705th most frequent Russian word.
шанхайской
"Shanghainese" or "of Shanghai."
шанхайской is used as an adjective to describe 'модной шляпой' (fashionable hat), attributing it with a 'Shanghai style' characteristic.
Она носила шанхайской модной шляпой.
She wore a Shanghai-style fashionable hat.
шанхайской is functioning as an adjective to specify 'технологией производства' (manufacturing technology), denoting its origin from or style associated with Shanghai.
Это было шанхайской технологией производства.
It was a Shanghai manufacturing technology.
шанхайской serves as an adjective describing 'живописи' (painting), indicating it pertains to a style or type associated with Shanghai.