The Microchip TC4422 is pin compatible and has somewhat lower output resistance. Some similar parts by IXYS are also pin compatible and have slightly better output resistance.
I assume you understand that total gate drive power is fixed for a given switching frequency, gate charge, and input voltage, irrespective of total gate resistance. All you can really expect to do is offload some of the heat away from the gate driver IC and into the gate resistor. You could keep the TC4420 part and just increase the gate resistance value, but then you would have slower switching performance. Alternatively you could replace the TC4420 with a lower resistance part like the TC4422 and then increase the gate resistor value a corresponding amount. In this way switching performance will not be altered (for the better or worse), but some of the heat will be offloaded from the driver IC and more into the gate resistor.
Alternatively you could replace your MOSFET(s)/IGBT(s) with lower gate charge device(s), or decrease the switching frequency, or decrease the gate drive voltage...