The only known (for today) japanese medal that was marked with Y is 1928 Showa Enthronement Commemorative Medal.
Thanks to the original paper wrappers we know who used this mark.
株式会社山崎商店 - Yamazaki Shop /Shoten/ Co., Ltd.
Y for Yamazaki
On the right we see a date
昭和參年拾貳月 - December 1928
Second known cariation of the wrapper bears different date.
昭和四年貳月- February 1929.