Can a Chevy 350 fit in a 1986 cutlass supreme that has a 350 0lds if so what will need to be replaced motor mount?

1984 Cutlass Supreme in 1984 was a G-body RWD car right?

The Gen1 to Gen3 Chevy small block including 350 will fit in any of these cars.

Transmission mating:

If original engine is Chevy V8 (usually 305 or 350) or Chevy V6 (229) no changes needed. Otherwise, a different bell housing or flywheel or torque converter may be required.

Mounting:

Go to an auto parts store and ask for motor mounts for your car, specify year make and model. Lie about the engine. Say it's a 305. 350 may not have been available for your car as OE, but 305 is a small block with the same mountings.

Carburetor:

Use an appropriate Quadrajet for your 350 and ECM to match the carb. Otherwise, a different carb can be used, but most won't provide the same combination of driveability/performance for street/strip applications.

Note that a 307 is an Oldslomobile engine and a 231 is a Buick engine both of which may require some minor changes to mountings and transmission mating.

An 86 olsmobile only came as a 307 or the smaller v6. If the car already has a bigger olsmobile engine in it then it should already be the same as a Chevy 350 although the numbers may not match (305 is the same as 307.)

You should have no problem putting in a 350.