The beta cells of the pancreas are the most commonly affected cells in a pancreas, when a person suffers from diabetes.
Pancreas are meant to regulate the sugar level in blood. This is achieved by the secretion of insulin. Beta cells are the cells in pancreas, which secrete insulin and help absorb sugar in blood and divert it to various required parts of the body.
When a person suffers from diabetes, the beta cells have to over-exert themselves, in order to produce more insulin. Eventually their capability to produce insulin is destroyed and they cease to function, leading to accumulation of sugar in the blood stream.
Also cells like, Alpha cells and Acini cells of the pancreas are affected, but these are a rarity. It is the Beta cells that are primarily affected.