I have a DNA match of 1,723 cM with a male 6 years younger than me. His father is one of a twin, could my match be not my half-sibling but my 1st cousin.
Given the 1723 cM number, I'm interpreting "his father is one of a twin" as "his father and my father are identical twins". This means that genetically, you and your first cousin are half-siblings.
The difference between genetic relationships and biological relationships is a nuance that the consumer DNA market ignores wholesale. If my child were to take a DNA test, all of the sites would claim a parent-child relationship with my sibling, with cheerful 100% certainty. (Just to make it clear: my sibling is childless, so all of the sites would be 100% wrong about the biological relationship.)
The Shared cM Project 4.0 tool v4 for 1,723cM does not suggest first cousin but it does suggest half-sibling. If grandparent, grandchild, niece/nephew and uncle/aunt are ruled out or considered unlikely based on your age difference then half sibling seems to be the most likely. Sibling is also a remote possibility.
Note that given the mention of twins in the question, this answer needs a strong disclaimer that it's talking only about genetic relationships, not biological or social ones.– JPmiaouMar 25, 2021 at 13:22