Cog/chain pitch

The Chain on my new bike (bianchi Pista) is supposed to be 1 1/8th so i went to my local shop to get a 17tooth 1 1/8th instead of the 16 thats on there. When i fitted the cog i put the wheel back on and put the chain onto the cog and the chain wouldnt sit on the cog properly, only about 3 of the teeth would sit in between the links and the others were sitting on top of the teeth. Have they given me the wrong size or is my chain a 3/32.

a 1/18 and a 3/32 chain will sit on a 3/32 cog, not the other way around.
so it must be 3/32 cog/chain and ring

Almost all chains, chainrings and cogs (all, except the odd but nice Dura Ace 10) have a 1/2" pitch (length of a chain link).

Width of chains is either 3/32" (narrow, for derailleur bikes) or 1/8" (for single speed, track, coaster brake, internally geared bikes)
Cogs and chain rings have teeth of either 2mm thickness (for 3/32" and 1/8" chains) or 3mm thickness (for 1/8" chains only).

first of all, the pitch has nothing to do with the width of the chain, it is how long the links are. secondly, there is no 1 and 1/8" chain. there are 1 and 1/8" headsets/steerer tubes.

according to evans the bianchi 2009 has a Kmc Z610H chain which is 3/32".

so it sounds like you've bought a 1/8" cog. so i would say you mistakenly thought your bike had a 1/8" chain when it actually has a 3/32" chain. solutions are new chain (1/8") or new cog (3/32").

Have they given me the wrong size or is my chain a 3/32.

Sounds like they have given you what you asked for (a 1/8 sprocket) but your chain is 3/32. Should be easy to tell as the old sprocket would be noticeably thinner than your new one if the old one is 3/32.

Well thats me being thick as fuck again and just glancing at the description before rushing out to get the sprocket.