I narrow it down to a contest between Fish and Fowl ( including chicken, turkey, duck etc). So who wins Or is there another vertebrate that pips these groupings.
By weight? By individual animals? Do we count eggs? Is beef in the same group as pork?
By individual animal.
Pig - pork is consumed by roughly 36% of the world population.
To clarify. A tiny shrimp and a large whale are still individuals and count as 1 each.
1 pig feeds a lot of people. Remember its not by weight but individual animal.
This source give the total amount of poultry consumed per year to be about 15 kg per person in 2013, or 105 billion kg for the world’s population of 7 billion.
Total meat consumption is given as about 34 kg per person per year. Subtracting the poultry leaves 19 kg, which would be almost entirely mammals (cattle, sheep, goats, pigs). That would give a total world consumption of around 133 billion kg per year.
This source gives the total production of fisheries and aquaculture as 158 million tonnes (1000 kg) per year, or 158 billion kg. Fisheries will, however, also include crustaceans and mollusks. Shrimp are probably the largest proportion of the shellfish portion of fisheries. From here, global shrimp production was around 2.4 million tons, or about 2.2 billion kg. Crabs, lobster, squid, clams, etc are probably each less. I think it’s unlikely all shellfish combined total more than 25 billion kg, so that consumption of vertebrate fish probably exceeds that of mammals, and certainly birds.
Then cree
Then certainly fish would be the answer. The average fish consumed weighs far less than mammals or birds used for food. Shrimp and mollusks weigh less individually than fish, but I doubt by enough to outnumber them.
The OP seems to be lumping large classes of animals rather than asking for individual species. I would assume all mammals would be included in one group.
NM
Your thread title specifies vertebrates. Shrimp are not vertebrates, so why mention them?
The OP was not a model of clarity in what was being asked.
Certainly there’s no ambiguity about mollusks, however. 
By animal? If it’s between fish and fowl, I’d say fish. We’ve probably eaten trillions of anchovies, sardines and pilchards, not to mention baby shrimp.
It takes a whole lot of shrimp to make one vertebrate.
D’oh! Nix the shrimp.
I thought goat was the most commonly eaten terrestrial animal, with the chicken in 2nd place?
Most societies eat fish and other aquatic creatures too.
Fish, definitely. Just think of the number of individual fish that go into making fish sauce and anchovy paste…
Which fish? Every type of fish is a different animal. Cod and salmon are as distinct as pig and cow.
Some sort of anchovy or sardine, most likely. Not the OP was that specific (if you’ll pardon the pun) having grouped all fish and all fowl.