python run asyncio task in the background

I want to run asynio task in the background so that below code prints out 'b' once while printing out 'a' recursively. Instead it prints 'a' forever with no 'b'.

It should cancel the task after 3 seconds like shown in the code.

I tried with create_task and event_loops with no success. Any help would be appreciated.

# SuperFastPython.com
# example of running an asyncio coroutine in the background
import asyncio
import time
import uuid


async def custom_coro():
    while True:
        print('a')
        time.sleep(1)
        # await asyncio.sleep(1)

async def run_ws():

    await asyncio.wait([
        custom_coro(),
    ])

if __name__ == '__main__':
    tasks = {}
    task = asyncio.run(run_ws())
    # task = asyncio.create_task(run_ws())

    task_id = str(uuid.uuid4())
    tasks[task_id] = task

    print('b')
    time.sleep(3)

    tasks[task_id].cancel()

    # tasks = asyncio.all_tasks()
    # t = tasks.pop()
    # t.cancel()

    # asyncio.run(run_ws())
    # print('b')

You cannot have time.sleep() in parallel with an async task. You can use something like this

import asyncio

async def custom_coro():
    while True:
        print('a')
        await asyncio.sleep(1)
    
task = asyncio.create_task(custom_coro())
print('b')
asyncio.gather(task)
await asyncio.sleep(3)
task.cancel()
print('done')

Output -

b
a
a
a
done
_GatheringFuture exception was never retrieved
future: <_GatheringFuture finished exception=CancelledError()>
concurrent.futures._base.CancelledError

wrapped in main function:

import asyncio

async def main():
    async def custom_coro():
        while True:
            print('a')
            await asyncio.sleep(1)

    task = asyncio.create_task(custom_coro())
    print('b')
    asyncio.gather(task)
    await asyncio.sleep(3)
    task.cancel()
    print('done')
    
asyncio.run(main())