#jlpt  n1

～が早いか     “No sooner than” Used when some action occurs shortly after another. Puts emphasis on the occurrence of two things happening almost at the same time. Cannot have volition, commands, or negatives follow. Formed with     V(ル・タ形) + が早いか

• 飼い主が名前を呼ぶが早いか、犬が走り出した

～ や否や（やいなや）“In response to A,  B suddenly happens.” One action follows on the heels of another and the second action is an unexpected reaction. Puts emphasis on the feeling of abruptness of the events. Cannot have volition, commands, or negatives follow. Formed with Ｖル＋ や否や/～否や/～や

• その薬を飲むや否や、急に眠気がおそってきた。
  

In a very quick way to differentiate these two,  ～が早いか emphasizes 同時に while   ～ や否や cannot attach to the past tense and emphasizes 突然に