Don't want to write this by hand? GodCraft sets minecraft:player.exhaustion for you with a switch.Get GodCraftOverview
minecraft:player.exhaustion is an entity component: it goes in the components object of a custom mob, or in one of its component groups. Tracks how tired the player is from actions like sprinting and jumping; when it fills up, saturation or hunger drops. Used by the player entity.
Example
Inside the components object of BP/entities/<name>.json (values are the defaults or placeholders):
BP/entities/<name>.json
{
"minecraft:player.exhaustion": {}
}