No one knows or will know until there is a DNA test. However judging from their pictures, I would pick Basil I because he had a similar nose to Leo VI compared to Michael III. Also, Basil being the first of his dynasty would most likely pick his biological son to continue the dynasty. For those reasons, Basil seems to be Leo's most plausible father.
I always it was Basil considering why he would choose Leo as his successor, I thought it would be somewhat odd and implausible for Basil putting the son of the man who killed for the throne as heir to Byzantium, just my two cents tho
Well, Basil's public heir was his first son Constantine, who was crowned in 868, a year after Basil became sole Emperor, and was noted to be the next in line until his early death in 879. Although Leo had been associated to the throne in 870, Basil didn't expect Constantine to die.
Not to mention the crappy relationship between the two; Basil even had Leo imprisoned for 3 years at one point...