If you want to go right into fellowship after residency, then it's around beginning to mid 2nd year. GI is pretty early, whereas Cards is more in the early fall/fall. The others fall somewhere between the two. Cards, GI, Pulm have matches and I'm not sure about renal, ID, etc.
A lot of people do a hospitalist year after residency to make $$ (175-250k are some of the offers people get from my residency program) and then start fellowship, so they apply during 3rd year.