Final answer:
The medial rectus muscle is the most likely cause of the patient's symptoms of double vision in certain fields of gaze.
Step-by-step explanation:
The extraocular muscle most likely to be causing the patient's symptoms of double vision in certain fields of gaze is the medial rectus muscle. The medial rectus muscle is responsible for inward movement of the eye, or adduction. When the medial rectus muscle is restricted or not functioning properly, it can result in the eyes not moving in perfect coordination, leading to double vision.