Could it be for this man?
World War I Draft Registration Cards, 1917-1918
Name: Edward J Patterson
City: Newark
County: Essex
State: New Jersey
Birthplace: Vermont;United States of America
Birth Date: 21 Jun 1890
Race: Caucasian (White)
Roll: 1754027
DraftBoard: 9
Occupation: New York Telephone Co., Telephone Engineer
Served 1 yr 6 months in the US Navy, but listed as a Private

There are no Privates in the Navy.
1920 Census shows him living in a Boarding House on Broad St. He was working again, for the New York Telephone Co and was Single.
Membership in the Knights of Columbus is open to practical Catholic men in union with the Holy See, who are at least 18 years old.
Most likely a Catholic Religious Medallion given to a service member and a Knights Member for their service to GOD and COUNTRY. Nice find! Hard to really see...pic is very tiny.