who took the mouths side of the snake that was used to churn the ocean of milk(the ocean of samudramanthan)

In the Samudra Manthan, the Asuras held the mouth/head end of Vasuki (the serpent used as the churning rope), while the Devas held the tail end. This was strategically assigned because the mouth end emitted more potent fumes and vapors during the churning process. Vishnu had suggested this arrangement to ensure the Asuras would bear the brunt of the toxic emissions.