0.5W Zener — the power rating that sets the current ceiling
The HZ12HB1 is a 0.5W Zener diode, meaning the maximum power it can dissipate in shunt regulation or clamping is half a watt. For a given Zener voltage, this sets the maximum continuous current: at 12 V, that's about 42 mA; at 5 V, about 100 mA. If your circuit needs to sink more current than that, you need a higher-power Zener or a different regulation scheme.
What the voltage rating is — and isn't
The available specifications for the HZ12HB1 list it as a 0.5W Zener diode, but they do not state the Zener voltage. If your BOM requires a specific Zener voltage, you will need to verify this against the manufacturer's datasheet or markings on the part before committing the line.