The L298 has one power input for the motors; you can supply either 12V or 24V in your situation.
Further it's a little outside my area of expertise.
The max power dissipation for the L298 is 25W; so it can do 24V at 1A or 12V at 2A.
If you only need one direction, use a logic level MosFet that suites tour needs; make sure it's a logic level one! In that case, don't forget a flyback diode. See e.g. https://www.gammon.com.au/motors for a schematic and explanations.