Step 1: Understand the structure of glycogen.
Glycogen is a highly branched polysaccharide that serves as the storage form of glucose in animals. It is composed entirely of glucose units.
Step 2: Identify the main chain linkage.
In glycogen, the linear chains of glucose molecules are connected mainly through
\[
\alpha(1\rightarrow4)
\]
glycosidic bonds.
Step 3: Understand branch formation.
At certain points, glycogen forms branches to increase solubility and allow rapid release of glucose during metabolism.
Step 4: Identify the bond at branch points.
The branch points are formed when a glucose unit is attached through an
\[
\alpha(1\rightarrow6)
\]
glycosidic linkage.
Step 5: Analyze option (A).
\(\alpha\)-1,4 glycosidic bonds are present in the straight chains, not at branch points. Hence, option (A) is incorrect.
Step 6: Analyze remaining options.
\(\beta\)-glycosidic bonds are characteristic of structural polysaccharides such as cellulose, not glycogen. Therefore, options (C) and (D) are incorrect.
Step 7: Final conclusion.
Thus, the bond formed at the branch point in glycogen is
\[
\boxed{\alpha\text{-1,6 glycosidic bond}}
\]
Hence, the correct answer is option (B).