What is the four letter abbreviation after the birds' names?

Each bird is given a four letter code which represents that species of bird. This code is called the AOU  Alpha Code (AOU = American Ornithologist Union).

Wondering what ASY, SY, AHY represents?

 It represents the age of the birds.

(every bird has a birthday on 31 December)

HY = Hatching Year

(indicates that a bird was hatched in the calendar year when it was banded until 31 December)

AHY = After Hatching Year

(a bird in at least its second calendar year especially after the breeding season when it implies an adult)

SY = Second Year

(a bird in its second calendar year.  i.e. 1 January of the year following fledging through 31 December of the same year)

ASY = After Second Year

(an adult in at least its third calendar year)