Simple RAW for 5e V: The Disadvantage Strikes Back

[E’Tallitnics]

Q56

Do all constructs wink out of existence in an Antimagic Field, since they were created by magic? If not, where can I read about this?

A56: Depends on the construct. Some are created by magic, while others are naturally occurring.

From the PH (Antimagic Field):
Creatures and Objects. A creature or object summoned or created by magic temporarily winks out of existence in the sphere. Such a creature instantly reappears once the space the creature occupied is no longer within the sphere.

From the MM (Creature Types):
Constructs are made, not born. Some are programmed by their creators to follow a simple set of instructions, while others are imbued with sentience and capable of independent thought. Golems are the iconic constructs. Many creatures native to the outer plane of Mechanus, such as modrons, are constructs shaped from the raw material of the plane by the will of more powerful creatures.

So a golem (creature type: construct; description: “Stone golems are magical constructs..." [Basic Rules, p.154]) would wink out of existence within the field, but a modron (creature type: construct; description: "...a new modron is created by Primus…" would not.

That being said, it's generally good advice to talk over any spell and especially a high level spell, with your DM to see how it works at their table.