Threw on my track team handed my baton to her
Passed her blew her off, I chronic Veronica
from Big Sean (Ft. Drake) – Made Lyrics on Rap Genius
Meaning
In the relays, there are batons that you pass to your teammates. He handed his dick (baton) to Veronica then he passed and blew her off (probably to a 3rd-tier dude in his entourage).
Maybe a stretch, but by mentioning “Vernonica,” Sean could be playing off of Drake’s Anchorman reference earlier in the song.

“For the entire Channel 4 news team, I’m Veronica Corningstone."
"And I’m Ron Burgundy. Go fuck yourself, San Diego.”
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