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1.
the carbonated cola soft drink Pepsi, as pronounced by some Asian-American restaurant employees and others who take a respectful liking to such dialectic pronunciation
"We have Pessi, Diet Pessi, 7-Up, Mountain Dew, hot tea, coffee, and water."

"Diet Coke? Diet Pessi okay?"
by Kevin_K July 30, 2006
 
2.
A soft drink served in American Chinese restaurants.
"Welcome to #1 China. We no have coke fount-ahh. You want Pessi?"
by Snoprano December 14, 2013