i have a 4-core cpu.can i code for specific cores in assembly?
like one core doing something and another doing something else.

Only if you use a low level OS or write your own, otherwise, you have to rely on your OS to schedule threads on two cores (which is usually what happens but not always). Or use OS-specific mechanisms to force it to do that (CPU affinity etc).

All mainstream OSes allow programs to set the affinity of each thread, and for the whole program. You can choose how to use it for what you need.