Debate has raged online among ornithologists as to the identity of the bird, with some believing it to be an extremely rare 'Hume's Leaf Warbler' - of which only about six will visit the UK from its native Asia on an average good year.
However, others think it is the Yellow Browed Warbler, still a "prize find" in the UK but several hundred of which visit each year from the Ural Mountains in Russia and Kazakhstan, and north-east China.
The bird, measuring less than four inches in length, was first spotted on November 8 near the Torness car park, and was still in the area last Friday (November 11) - when it attracted the interest of Darren Woodhead, Haddington wildlife artist.
Two other Hume's were reported to have been spotted last week in Shetland and the south of England.
Penicuik photographer Mike Thrower snapped the bird last Wednesday. He said: "The bird in question has plumage that occurs on both birds, making the identification a bit of a nightmare.
"Since last Wednesday, its call has been taped and my photographs studied all over the country by members of rarities committees in Scotland and the majority feel that this is an unusual Yellow Browed Warbler."