Step 1: Recall the bond types in oxoacids.
Phosphorus oxoacids can have $P=O$ bonds, $P-OH$ bonds, $P-H$ bonds, $P-O-P$ bridges, or peroxy $P-O-O-P$ linkages. We are looking for the peroxy one.
Step 2: Define a peroxy linkage.
A peroxy linkage is two oxygen atoms joined directly together, $-O-O-$, each oxygen in the $-1$ state.
Step 3: Check orthophosphoric acid.
Orthophosphoric acid $H_3PO_4$ has only $P=O$ and $P-OH$ bonds, no peroxy bond.
Step 4: Check pyrophosphoric acid.
Pyrophosphoric acid $H_4P_2O_7$ has a single oxygen bridge $P-O-P$, but that is not a peroxy bond.
Step 5: Check peroxodiphosphoric and hypophosphoric acids.
Peroxodiphosphoric acid $H_4P_2O_8$ has the $P-O-O-P$ peroxy bridge, just as its name suggests. Hypophosphoric acid $H_4P_2O_6$ has a direct $P-P$ bond, not peroxy.
Step 6: Pick the answer.
So the peroxy linkage is found in peroxodiphosphoric acid. \[ \boxed{\text{Peroxodiphosphoric acid}} \]