Hello,
All the links that you provide seem to refer to small electro-mechanical relays, rather than to a "solid-state" relay type. For the 3 volt type, these would typically require a coil current in the region of 50ma (which seems overkill for a 320 mA load current). This coil current is too high for a direct interface to a MCU GPIO pin, so you will need an external bipolar transistor or MOSFET driver. This will need the usual protection required to absorb switching transients due to the relay coil inductance.
As Rocco has already suggested, the output of the driver might be used to directly switch the modem supply, but you would need to tolerate "low side" switching, also with common ground connections for the MCU supply and the modem supply. Another alternative might be to find a "high side" switch driver device, if high side switching is required, but the ground connections can remain common.
A fully isolated solution will require the use of an electro-mechanical relay, or a solid-state relay type. For the latter type, sufficient current capability will be required to drive the input of an opto-coupler, so the transistor driver may still be necessary. Note that you will require a SS relay specifically intended for DC operation. The more common AC type is not suitable.
To reduce the coil current of the electro-mechanical relay, one that operates at a higher voltage might be considered. However, if providing power from the modem supply, the range 9-28 volt would likely be excessive.
If you were able to make use of this supply in order to use a SS relay with a higher minimum activation voltage (which may be easier to obtain), you might consider arranging a bi-polar transistor driver as a constant current source for the relay, independent of the supply voltage range. You might select a 5 volt SS relay type, and provide a constant current to produce 5 volt across the relay input. A constant current is achieved by fitting a resistor between transistor emitter and ground, and removing any current limiting resistor in the base circuit. About 2.3 volts should appear accros the emitter resistor. A Darlington transistor must not be used.
In summary, the solution will depend on whether you require high side switching, and whether there is a common ground between the MCU and the modem power supplies.
Regards,
Mac